{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (<; >; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="],[">"],["<"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <table><tr><th>Cho h\u00ecnh v\u1ebd<br><\/th><th> So s\u00e1nh hai cung <br><\/th><\/tr><tr><td>a. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D1.1.png' \/><\/center> <br\/> Bi\u1ebft $AB\/\/CD$ <br><\/td><td>$\\overset\\frown{AC}$_input_$\\overset\\frown{BD}$<\/td><\/tr><tr><td> b. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D1.2.png' \/><\/center> <br><\/td><td>$\\overset\\frown{AB}$_input_ $\\overset\\frown{CD}$<\/td><\/tr><tr><td>c. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D1.3.png' \/><\/center> <\/td><td>$\\overset\\frown{DE}$_input_ $\\overset\\frown{EF}$<\/td><\/tr><\/table>","explain":"<span class='basic_left'> $a.$ <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D1.4.png' \/><\/center> <br\/> Qua $O$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $AB$ v\u00e0 $CD$, c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $E$ v\u00e0 $F$ <br\/> Do $AB \/\/ EF$ $\\Rightarrow \\left\\{ \\begin{align} & \\widehat{OAB}=\\widehat{{{O}_{1}}} \\\\ & \\widehat{OBA}=\\widehat{{{O}_{2}}} \\\\ \\end{align} \\right.$ (hai c\u1eb7p g\u00f3c sole trong) <br\/> X\u00e9t $\\Delta OAB$ c\u00f3: $OA=OB=R$ <br\/> $\\Rightarrow \\Delta OAB$ c\u00e2n t\u1ea1i $O$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{OAB}=\\widehat{OBA}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}=\\widehat{{{O}_{2}}}$ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: $ \\widehat{{{O}_{3}}}=\\widehat{{{O}_{4}}}$ <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}+\\widehat{{{O}_{3}}} = \\widehat{{{O}_{2}}} + \\widehat{{{O}_{4}}}$ hay $ \\widehat{AOC}=\\widehat{BOD}$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AC} = \\text{s\u0111}\\overset\\frown{BD}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow \\overset\\frown{AC} = \\overset\\frown{BD}$ <br\/>$b.$ Do $AB > CD \\Rightarrow \\overset\\frown{AB} > \\overset\\frown{CD}$ <br\/> $c.$ Do $DE < EF \\Rightarrow \\overset\\frown{DE} < \\overset\\frown{EF}$ <br\/> <span class='basic_pink'>V\u1eady c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $=; >; <$<\/span> <\/span> "}]}],"id_ques":1441},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","temp":"true_false","correct":[["t","f","t","f"]],"list":[{"point":5,"col_name":["","\u0110\u00fang","Sai"],"arr_ques":["V\u1edbi hai cung nh\u1ecf trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, hai cung b\u1eb1ng nhau c\u0103ng hai d\u00e2y b\u1eb1ng nhau ","V\u1edbi hai cung nh\u1ecf, hai d\u00e2y b\u1eb1ng nhau c\u0103ng hai cung b\u1eb1ng nhau","V\u1edbi hai cung nh\u1ecf trong hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau, cung l\u1edbn h\u01a1n c\u0103ng d\u00e2y l\u1edbn h\u01a1n","V\u1edbi hai cung nh\u1ecf, d\u00e2y c\u00e0ng l\u1edbn c\u0103ng cung c\u00e0ng l\u1edbn "],"explain":["\u0110\u00fang, v\u00ec theo \u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y","<br\/>Sai, v\u00ec hai d\u00e2y c\u00f3 th\u1ec3 kh\u00f4ng thu\u1ed9c c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ho\u1eb7c hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau","<br\/>\u0110\u00fang, v\u00ec theo \u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y","<br\/>Sai, v\u00ec hai d\u00e2y c\u00f3 th\u1ec3 kh\u00f4ng thu\u1ed9c c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ho\u1eb7c hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau"]}]}],"id_ques":1442},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho $\\Delta ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $\\left( O \\right)$ c\u00f3 $\\widehat{A}={{80}^{o}};\\widehat{B}={{60}^{o}}$. H\u00e3y so s\u00e1nh c\u00e1c cung $\\overset\\frown{AB};\\overset\\frown{AC};\\overset\\frown{BC}.$ ","select":["A. $\\overset\\frown{BC}>\\overset\\frown{AB}>\\overset\\frown{AC}$ ","B. $\\overset\\frown{BC}>\\overset\\frown{AC}>\\overset\\frown{AB}$ ","C. $\\overset\\frown{AB}>\\overset\\frown{AC}>\\overset\\frown{BC}$","D. $\\overset\\frown{AC}>\\overset\\frown{AB}>\\overset\\frown{BC}$"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D3.png' \/><\/center> X\u00e9t $\\Delta ABC$ c\u00f3: <br\/> $\\widehat{A}+\\widehat{B}+\\widehat{C}={{180}^{o}}$ (t\u1ed5ng ba g\u00f3c c\u1ee7a tam gi\u00e1c) <br\/> $\\Rightarrow \\widehat{C}={{180}^{o}}-\\widehat{A}-\\widehat{B}$ <br\/> $\\hspace{1,2cm} ={{180}^{o}}-{{80}^{o}}-{{60}^{o}}={{40}^{o}}$ <br\/> $\\Rightarrow \\widehat{C} < \\widehat{B} < \\widehat{A}$ <br\/> $\\Rightarrow AB < AC < BC$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong tam gi\u00e1c) <br\/> $\\Rightarrow \\overset\\frown{AB} < \\overset\\frown{AC} < \\overset\\frown{BC}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":2}]}],"id_ques":1443},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $\\left( O;R \\right)$, c\u00f3 b\u1ed1n \u0111i\u1ec3m $A, \\,B,\\,C, \\, D$ ph\u00e2n bi\u1ec7t th\u1ecfa m\u00e3n $AB=BC=CD=DA$. \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng $AB$ l\u00e0:","select":["A. $R$ ","B. $R\\sqrt{2}$ ","C. $R\\sqrt{3}$ ","D. $2R$"],"hint":"T\u00ednh s\u1ed1 \u0111o g\u00f3c $AOB$ r\u1ed3i t\u1eeb \u0111\u00f3 suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh $AB$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D4.png' \/><\/center> <br\/> Ta c\u00f3: $AB=BC=CD=DA$ <br\/> $\\Rightarrow \\overset\\frown{AB}=\\overset\\frown{BC}=\\overset\\frown{CD}=\\overset\\frown{DA}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> M\u00e0 $\\text{s\u0111}\\overset\\frown{AB}+\\text{s\u0111}\\overset\\frown{BC}+\\text{s\u0111}\\overset\\frown{CD}+\\text{s\u0111}\\overset\\frown{DA}={{360}^{o}}$ <br\/> $\\Rightarrow 4.\\text{s\u0111}\\overset\\frown{AB}={{360}^{o}}$ $\\Rightarrow \\text{s\u0111}\\overset\\frown{AB}={{90}^{o}}$ <br\/> $\\Rightarrow \\widehat{AOB}={{90}^{o}}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> X\u00e9t $\\Delta OAB$ vu\u00f4ng t\u1ea1i $O$ c\u00f3: <br\/> $A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow A{{B}^{2}}={{R}^{2}}+{{R}^{2}}=2{{R}^{2}}$ <br\/> $\\Rightarrow AB=R\\sqrt{2}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":4}]}],"id_ques":1444},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'> Tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $\\left( O;R \\right)$ c\u00f3 hai d\u00e2y cung $MN$ v\u00e0 $PQ$, bi\u1ebft $MN = PQ$. H\u00e3y so s\u00e1nh hai g\u00f3c \u1edf t\u00e2m $\\widehat{MON}$ v\u00e0 $\\widehat{POQ}$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{MON}$ _input_ $\\widehat{POQ}$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D5.png' \/><\/center> <br\/> Ta c\u00f3: $MN=PQ$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\overset\\frown{MN}=\\overset\\frown{PQ}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{MN}=\\text{s\u0111}\\overset\\frown{PQ}$ <br\/> $\\Rightarrow \\widehat{MON}=\\widehat{POQ}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$<\/span> <\/span>"}]}],"id_ques":1445},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="],[">"],["<"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'>Cho h\u00ecnh v\u1ebd <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D6.png' \/><\/center> <br\/> $MN$ l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng k\u00ednh, $OE\\bot MN$. H\u00e3y so s\u00e1nh \u0111\u1ed9 d\u00e0i c\u00e1c d\u00e2y <br\/> a. $ME$ _input_ $NE$ <br\/> b. $ME$ _input_ $NF$ <br\/> c. $EN$ _input_ $MF$ ","explain":" <span class='basic_left'> a. Ta c\u00f3: $\\widehat{MOE}=\\widehat{NOE}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{ME}=\\text{s\u0111}\\overset\\frown{NE}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow ME=NE$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> b. Ta c\u00f3: $\\widehat{MOE}={{90}^{o}};\\widehat{NOF}<{{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{MOE}>\\widehat{NOF}\\Rightarrow \\text{s\u0111}\\overset\\frown{ME} > \\text{s\u0111}\\overset\\frown{NF}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow ME > NF$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> c. Ta c\u00f3: $\\widehat{EON}={{90}^{o}};\\widehat{MOF}>{{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{EON}<\\widehat{MOF}\\Rightarrow \\text{s\u0111}\\overset\\frown{EN} < \\text{s\u0111}\\overset\\frown{MF}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow EN < MF$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> <span class='basic_pink'> V\u1eady c\u00e1c d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $=; > ; <$ <\/span><\/span> "}]}],"id_ques":1446},{"time":24,"part":[{"time":3,"title":"Cho tam gi\u00e1c c\u00e2n $ABC$ c\u00e2n t\u1ea1i $A$. Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $BA$ l\u1ea5y \u0111i\u1ec3m $D$, v\u1ebd \u0111\u01b0\u1eddng tr\u00f2n $(O)$ ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $BCD$. Qua $O$ k\u1ebb $OH; OK$ l\u1ea7n l\u01b0\u1ee3t vu\u00f4ng g\u00f3c v\u1edbi $CD$ v\u00e0 $BC$ ($H\\in DC, \\,K\\in BC$). Ch\u1ee9ng minh $OH < OK$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[3],[5],[1],[4]]],"list":[{"point":5,"left":["M\u00e0 $\\widehat{DBC}+\\widehat{ABC}={{180}^{o}}$ (hai g\u00f3c k\u1ec1 b\u00f9) $\\Rightarrow \\widehat{DBC}>{{90}^{o}}$","X\u00e9t $\\Delta BDC$ c\u00f3: $\\widehat{B}>{{90}^{o}}$ (ch\u1ee9ng minh tr\u00ean)","$\\Rightarrow OH < OK$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y)","Do $\\Delta ABC$ c\u00e2n t\u1ea1i $A$ $\\Rightarrow \\widehat{ABC}<{{90}^{o}}$ ","$\\Rightarrow \\widehat{B}>\\widehat{D}\\Rightarrow DC>BC$ (quan h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c)"],"top":55,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D7.png' \/><\/center> <br\/> Do $\\Delta ABC$ c\u00e2n t\u1ea1i $A$ <br\/> $\\Rightarrow \\widehat{ABC}<{{90}^{o}}$ <br\/> M\u00e0 $\\widehat{DBC}+\\widehat{ABC}={{180}^{o}}$ (hai g\u00f3c k\u1ec1 b\u00f9) <br\/> $\\Rightarrow \\widehat{DBC}>{{90}^{o}}$ <br\/> X\u00e9t $\\Delta BDC$ c\u00f3: <br\/> $\\widehat{B}>{{90}^{o}}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow \\widehat{B}>\\widehat{D}\\Rightarrow DC>BC$ (quan h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c) <br\/> $\\Rightarrow OH < OK$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <\/span>"}]}],"id_ques":1447},{"time":24,"part":[{"time":3,"title":"Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AE$. G\u1ecdi $B, C, D$ l\u00e0 ba \u0111i\u1ec3m tr\u00ean n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n sao cho $\\overset\\frown{AC}=2\\overset\\frown{AB};\\overset\\frown{AD}=3\\overset\\frown{AB}.$ Ch\u1ee9ng minh $AB = BC = CD$.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[3],[5],[1],[4],[2]]],"list":[{"point":5,"left":["$\\text{s\u0111}\\overset\\frown{AD}=\\text{s\u0111}\\overset\\frown{AC}+\\text{s\u0111}\\overset\\frown{CD}$ ($C$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $D$)","T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\overset\\frown{AB}=\\overset\\frown{BC}=\\overset\\frown{CD}$ <br\/> $\\Rightarrow AB=BC=CD$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y)","Ta c\u00f3: $\\text{s\u0111}\\overset\\frown{AC}=\\text{s\u0111}\\overset\\frown{AB}+\\text{s\u0111}\\overset\\frown{BC}$ ($B$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $C$) ","$\\Rightarrow \\text{s\u0111}\\overset\\frown{CD}=\\text{s\u0111}\\overset\\frown{AD}-\\text{s\u0111}\\overset\\frown{AC}=3\\text{s\u0111}\\overset\\frown{AB}-2\\text{s\u0111}\\overset\\frown{AB}=\\text{s\u0111}\\overset\\frown{AB}$ (2) ","$\\Rightarrow \\text{s\u0111}\\overset\\frown{BC}=\\text{s\u0111}\\overset\\frown{AC}-\\text{s\u0111}\\overset\\frown{AB}=2\\text{s\u0111}\\overset\\frown{AB}-\\text{s\u0111}\\overset\\frown{AB}=\\text{s\u0111}\\overset\\frown{AB}$ (1)"],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D8.png' \/><\/center> <br\/> Ta c\u00f3: $\\text{s\u0111}\\overset\\frown{AC}=\\text{s\u0111}\\overset\\frown{AB}+\\text{s\u0111}\\overset\\frown{BC}$ ($B$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $C$) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{BC}=\\text{s\u0111}\\overset\\frown{AC}-\\text{s\u0111}\\overset\\frown{AB}=2\\text{s\u0111}\\overset\\frown{AB}-\\text{s\u0111}\\overset\\frown{AB}=\\text{s\u0111}\\overset\\frown{AB}$ (1) <br\/> $\\text{s\u0111}\\overset\\frown{AD}=\\text{s\u0111}\\overset\\frown{AC}+\\text{s\u0111}\\overset\\frown{CD}$ ($C$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $D$) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{CD}=\\text{s\u0111}\\overset\\frown{AD}-\\text{s\u0111}\\overset\\frown{AC}=3\\text{s\u0111}\\overset\\frown{AB}-2\\text{s\u0111}\\overset\\frown{AB}=\\text{s\u0111}\\overset\\frown{AB}$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\overset\\frown{AB}=\\overset\\frown{BC}=\\overset\\frown{CD}$$\\Rightarrow AB=BC=CD$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <\/span>"}]}],"id_ques":1448},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'> Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$, \u0111\u01b0\u1eddng k\u00ednh $AB$, v\u1ebd d\u00e2y $CD \/\/ AB$. H\u00e3y so s\u00e1nh $\\overset\\frown{AC}\\,$v\u00e0 $\\overset\\frown{BD}$. <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $\\overset\\frown{AC}\\,$ _input_ $\\overset\\frown{BD}$ ","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D9.png' \/><\/center> Do $AB \/\/ CD$ <br\/> $\\Rightarrow \\left\\{ \\begin{align} & \\widehat{OCD}=\\widehat{{{O}_{1}}} \\\\ & \\widehat{ODC}=\\widehat{{{O}_{2}}} \\\\ \\end{align} \\right.$ (hai c\u1eb7p g\u00f3c sole trong) <br\/> X\u00e9t $\\Delta OCD$ c\u00f3: <br\/> $OC=OD=R$ <br\/> $\\Rightarrow \\Delta OCD$ c\u00e2n t\u1ea1i $O$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{OCD}=\\widehat{ODC}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}=\\widehat{{{O}_{2}}}$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AC}=\\text{s\u0111}\\overset\\frown{BD}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) hay $\\overset\\frown{AC}=\\overset\\frown{BD}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$ <\/span><br\/> <b> Ch\u00fa \u00fd: <\/b> Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song th\u00ec b\u1eb1ng nhau<\/span> "}]}],"id_ques":1449},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; r)$ v\u1edbi d\u00e2y cung $AB$. G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $I$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ee7a cung $AB$. Ch\u1ee9ng minh ba \u0111i\u1ec3m $H,\\, I,\\, O$ th\u1eb3ng h\u00e0ng.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[3],[1],[5],[4],[2]]],"list":[{"point":5,"left":["M\u00e0 $OA=OB=r$ $\\Rightarrow O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$","Ta c\u00f3: $\\overset\\frown{IA}=\\overset\\frown{IB}$ ($I$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa $\\overset\\frown{AB}$) ","Suy ra ba \u0111i\u1ec3m $H,\\, I,\\, O$ th\u1eb3ng h\u00e0ng ","Suy ra $OI$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AB$ $\\Rightarrow \\,H$ n\u1eb1m tr\u00ean $OI$ ($H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$) ","$\\Rightarrow IA=IB$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> $\\Rightarrow I$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D10.png' \/><\/center> <br\/> Ta c\u00f3: $\\overset\\frown{IA}=\\overset\\frown{IB}$ ($I$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa $\\overset\\frown{AB}$) <br\/> $\\Rightarrow IA=IB$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> $\\Rightarrow I$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> M\u00e0 $OA=OB=r$ <br\/> $\\Rightarrow O$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> Suy ra $OI$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AB$ <br\/> $\\Rightarrow \\,H$ n\u1eb1m tr\u00ean $OI$ ($H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$) <br\/> Suy ra ba \u0111i\u1ec3m $H,\\, I,\\, O$ th\u1eb3ng h\u00e0ng <\/span>"}]}],"id_ques":1450},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (<; >; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'> Cho hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau $(O)$ v\u00e0 $(O\u2019)$ c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m $A, B$. K\u1ebb c\u00e1c \u0111\u01b0\u1eddng k\u00ednh $AOC$ v\u00e0 $AO\u2019D$. <br\/> <b> C\u00e2u 1: <\/b> H\u00e3y so s\u00e1nh c\u00e1c cung nh\u1ecf $\\overset\\frown{BC}\\,$ v\u00e0 $\\overset\\frown{BD}$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\overset\\frown{BC}\\,$ _input_ $\\overset\\frown{BD}$ ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D11.png' \/><\/center> <br\/> X\u00e9t $\\Delta ABC$ c\u00f3: <br\/> $OA=OB=OC$ (c\u00f9ng b\u1eb1ng b\u00e1n k\u00ednh c\u1ee7a $(O)$) <br\/> $\\Rightarrow \\Delta ABC$ vu\u00f4ng t\u1ea1i $B$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{ABC}={{90}^{o}}$ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta \u0111\u01b0\u1ee3c: $\\widehat{ABD}={{90}^{o}}$ <br\/> $\\Rightarrow \\widehat{ABC}+\\widehat{ABD}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$ <br\/> $\\Rightarrow C,\\,B,\\,D$ th\u1eb3ng h\u00e0ng <br\/> $\\Rightarrow AB\\bot CD$ <br\/> X\u00e9t $\\Delta CAD$ c\u00f3: <br\/> $AC=AD$ ($\\left( O \\right)$ v\u00e0 $\\,\\left( O' \\right)$ c\u00f9ng b\u00e1n k\u00ednh) <br\/> $\\Rightarrow \\Delta ACD$ c\u00e2n t\u1ea1i $A$ <br\/> M\u00e0 $AB\\bot CD$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow CB=BD$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao trong tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\overset\\frown{BC}=\\overset\\frown{BD}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$<\/span> <\/span> "}]}],"id_ques":1451},{"time":24,"part":[{"time":3,"title":"Cho hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau $(O)$ v\u00e0 $(O\u2019)$ c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m $A, B$. K\u1ebb c\u00e1c \u0111\u01b0\u1eddng k\u00ednh $AOC$ v\u00e0 $AO\u2019D$. <br\/> <b> C\u00e2u 2: <\/b> G\u1ecdi $E$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng $AC$ v\u1edbi $(O\u2019)$. Ch\u1ee9ng minh r\u1eb1ng $B$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa $\\overset\\frown{EBD}$.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[4],[6],[5],[1],[3]]],"list":[{"point":5,"left":["$\\Rightarrow \\Delta AED$ vu\u00f4ng t\u1ea1i $E$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) "," $\\Rightarrow BC=BD=BE$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) ","$\\Rightarrow B$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa $\\overset\\frown{EBD}$"," $\\Rightarrow \\overset\\frown{BE}=\\overset\\frown{BD}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) "," X\u00e9t $\\Delta AED$ c\u00f3: $O'A=O'E=O'D$ (c\u00f9ng b\u1eb1ng b\u00e1n k\u00ednh $\\left( O' \\right)$) ","X\u00e9t $\\Delta CED$ vu\u00f4ng t\u1ea1i $E$ c\u00f3: $BC=BD$ (theo c\u00e2u 1) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D12.png' \/><\/center> <br\/> X\u00e9t $\\Delta AED$ c\u00f3: <br\/> $O'A=O'E=O'D$ (c\u00f9ng b\u1eb1ng b\u00e1n k\u00ednh $\\left( O' \\right)$) <br\/> $\\Rightarrow \\Delta AED$ vu\u00f4ng t\u1ea1i $E$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> X\u00e9t $\\Delta CED$ vu\u00f4ng t\u1ea1i $E$ c\u00f3: <br\/> $BC=BD$ (theo c\u00e2u 1) <br\/> $\\Rightarrow BC=BD=BE$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\overset\\frown{BE}=\\overset\\frown{BD}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> $\\Rightarrow B$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa $\\overset\\frown{EBD}$ <\/span>"}]}],"id_ques":1452},{"time":24,"part":[{"time":3,"title":"Tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$ l\u1ea5y hai \u0111i\u1ec3m $C, D.$ T\u1eeb $C$ k\u1ebb $CH\\bot AB$, n\u00f3 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $E.$ T\u1eeb $A$ k\u1ebb $AK\\bot DC$ n\u00f3 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $F.$ <b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh hai cung nh\u1ecf $CF$ v\u00e0 $DB$ b\u1eb1ng nhau.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[1],[3],[5],[4],[2]]],"list":[{"point":5,"left":["X\u00e9t $\\Delta AFB$ c\u00f3: $OA=OB=OF=\\dfrac{AB}{2}$ "," $\\Rightarrow AF\\bot BF\\Rightarrow AK\\bot BF$ "," $\\Rightarrow \\overset\\frown{FC}=\\overset\\frown{BD}$ (hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song) "," M\u00e0 $AK\\bot CD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow BF\/\/CD$ (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) ","$\\Rightarrow \\Delta AFB$ vu\u00f4ng t\u1ea1i $F$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D13.png' \/><\/center> <br\/> X\u00e9t $\\Delta AFB$ c\u00f3: <br\/> $OA=OB=OF=\\dfrac{AB}{2}$ <br\/> $\\Rightarrow \\Delta AFB$ vu\u00f4ng t\u1ea1i $F$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AF\\bot BF$ $\\Rightarrow AK\\bot BF$ <br\/> M\u00e0 $AK\\bot CD$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow BF\/\/CD$ (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/> $\\Rightarrow \\overset\\frown{FC}=\\overset\\frown{BD}$ (hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song) <\/span>"}]}],"id_ques":1453},{"time":24,"part":[{"time":3,"title":"Tr\u00ean n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$ l\u1ea5y hai \u0111i\u1ec3m $C, D.$ T\u1eeb $C$ k\u1ebb $CH\\bot AB$, n\u00f3 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $E.$ T\u1eeb $A$ k\u1ebb $AK\\bot DC$ n\u00f3 c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $F.$ <b> C\u00e2u 2: <\/b> Ch\u1ee9ng minh $BF=DE$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[5],[3],[1],[2]]],"list":[{"point":5,"left":["M\u00e0 $\\overset\\frown{DB}=\\overset\\frown{CF}$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\overset\\frown{BC}+\\overset\\frown{CF}=\\overset\\frown{BE}+\\overset\\frown{BD}\\,hay\\,\\overset\\frown{BF}=\\overset\\frown{DE}$ ","$\\Rightarrow BF=DE$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y)"," $\\Rightarrow \\Delta CBE$ c\u00e2n t\u1ea1i $B$ $\\Rightarrow BC=BE$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\overset\\frown{BC}=\\overset\\frown{BE}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) "," Ta c\u00f3: $CE\\bot AB$ <br\/> $\\Rightarrow CH=HE$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) ","X\u00e9t $\\Delta CBE$ c\u00f3: $\\left\\{ \\begin{align} & BH\\bot CE\\,\\left( \\text{gi\u1ea3 thi\u1ebft} \\right) \\\\ & CH=HE\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ \\end{align} \\right.$ "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D14.png' \/><\/center> <br\/> Ta c\u00f3: $CE\\bot AB$ <br\/> $\\Rightarrow CH=HE$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> X\u00e9t $\\Delta CBE$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & BH\\bot CE\\,\\left( \\text{gi\u1ea3 thi\u1ebft} \\right) \\\\ & CH=HE\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta CBE$ c\u00e2n t\u1ea1i $B$ <br\/> $\\Rightarrow BC=BE$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\overset\\frown{BC}=\\overset\\frown{BE}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> M\u00e0 $\\overset\\frown{DB}=\\overset\\frown{CF}$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\overset\\frown{BC}+\\overset\\frown{CF}=\\overset\\frown{BE}+\\overset\\frown{BD}$ hay $\\overset\\frown{BF}=\\overset\\frown{DE}$ <br\/> $\\Rightarrow BF=DE$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <\/span>"}]}],"id_ques":1454},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'> Cho tam gi\u00e1c $ABC$ c\u00f3 trung tuy\u1ebfn $AM$ v\u00e0 \u0111\u01b0\u1eddng cao $BH.$ V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111i\u1ec3m $C, \\, M, \\, H.$ H\u00e3y so s\u00e1nh c\u00e1c cung nh\u1ecf $MH$ v\u00e0 $MC$. <br\/> <b> \u0110\u00e1p s\u1ed1 <\/b> $\\overset\\frown{MH}$ _input_ $\\overset\\frown{MC}$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D15.png' \/><\/center> <br\/> X\u00e9t $\\Delta BHC$vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $BM=MC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow BM=MC=HM$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\overset\\frown{MH}=\\overset\\frown{MC}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$<\/span> <\/span>"}]}],"id_ques":1455},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["120"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O; 2R)$. T\u1eeb $M\\in \\left( O;2R \\right)$ k\u1ebb hai ti\u1ebfp tuy\u1ebfn $MA, MB$ \u0111\u1ebfn $(O; R)$ ($A, B$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). C\u00e1c ti\u1ebfp tuy\u1ebfn n\u00e0y c\u1eaft $(O; 2R)$ t\u1ea1i $N$ v\u00e0 $K.$ <br\/> <b> C\u00e2u 1: <\/b> S\u1ed1 \u0111o cung $AB$ b\u1eb1ng _input_ $^o$ ","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D16.png' \/><\/center> <br\/> Ta c\u00f3: $\\left\\{ \\begin{align} & \\widehat{OAM}={{90}^{o}} \\\\ & \\widehat{OBM}={{90}^{o}} \\\\ \\end{align} \\right.$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) <br\/> $MO$ l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $\\widehat{AMB}$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> X\u00e9t $\\Delta OAM$ vu\u00f4ng t\u1ea1i $A$ c\u00f3: <br\/> $\\sin \\widehat{AMO}=\\dfrac{OA}{OM}=\\dfrac{R}{2R}=\\dfrac{1}{2}$ <br\/> $\\Rightarrow \\widehat{AMO}={{30}^{o}}$ <br\/> $\\Rightarrow \\widehat{AMB}={{2.30}^{o}}={{60}^{o}}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c) <br\/> M\u00e0 $\\widehat{AMB}+\\widehat{MBO}+\\widehat{BOA}+\\widehat{OAM}={{360}^{o}}$ <br\/> $\\Rightarrow \\widehat{AOB}={{360}^{o}}-\\left( \\widehat{AMB}+\\widehat{MBO}+\\widehat{OAM} \\right)$ <br\/> $\\hspace{1,5cm}={{360}^{o}}-\\left( {{60}^{o}}+{{90}^{o}}+{{90}^{o}} \\right)={{120}^{o}}$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AB}={{120}^{o}}$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $120$ <\/span><\/span> "}]}],"id_ques":1456},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O; 2R)$. T\u1eeb $M\\in \\left( O;2R \\right)$ k\u1ebb hai ti\u1ebfp tuy\u1ebfn $MA, MB$ \u0111\u1ebfn $(O; R),$ c\u00e1c ti\u1ebfp tuy\u1ebfn n\u00e0y c\u1eaft $(O; 2R)$ t\u1ea1i $N$ v\u00e0 $K.$ <br\/> <b> C\u00e2u 2: <\/b> So s\u00e1nh hai cung $MN$ v\u00e0 $NK$. <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\overset\\frown{MN}$ _input_ $\\overset\\frown{NK}$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D17.png' \/><\/center> Ta c\u00f3: $OA=R;OM=2R$ (gi\u1ea3 thi\u1ebft) <br\/> X\u00e9t $\\Delta OAM$ vu\u00f4ng t\u1ea1i $A$ c\u00f3: <br\/>$O{{M}^{2}}=O{{A}^{2}}+A{{M}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow A{{M}^{2}}=O{{M}^{2}}-O{{A}^{2}}=4{{R}^{2}}-{{R}^{2}}=3{{R}^{2}}$ <br\/> $\\Rightarrow AM=R\\sqrt{3}$ <br\/> M\u00e0 $OA\\bot MN\\Rightarrow MA=AN$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow MN=2MA=2R\\sqrt{3}$ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: $MK=2R\\sqrt{3}$ <br\/> $\\widehat{NMK}={{60}^{o}}$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\Delta MNK$ \u0111\u1ec1u (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow MN=NK$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c \u0111\u1ec1u) <br\/> $\\Rightarrow \\overset\\frown{MN}=\\overset\\frown{NK}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$ <\/span> <\/span> "}]}],"id_ques":1457},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["9"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O),$ \u0111\u01b0\u1eddng k\u00ednh $AB= 25 cm.$ K\u1ebb d\u00e2y $CD$ song song v\u1edbi $AB \\, (C$ thu\u1ed9c cung $AD), CD= 7cm.$ K\u1ebb $CH$ vu\u00f4ng g\u00f3c v\u1edbi $AB. $ \u0110\u1ed9 d\u00e0i $AH$ l\u00e0 _input_ $(cm)$ ","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D18.png' \/><\/center> <br\/> Ta c\u00f3 $CD\/\/AB$ <br\/> $\\Rightarrow $ $\\overset\\frown{AC}=\\overset\\frown{BD}$ (hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song) <br\/> $\\Rightarrow AC=BD$ (li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> K\u1ebb $DK\\bot AB$, ta c\u00f3 $CD\/\/AB\\Rightarrow ACDB$ l\u00e0 h\u00ecnh thang <br\/> $\\Rightarrow CH=DK$ (c\u00f9ng b\u1eb1ng chi\u1ec1u cao h\u00ecnh thang) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $ \\Delta ACH$ v\u00e0 $\\Delta BDK$ c\u00f3: $\\left\\{ \\begin{align} & AC = BD \\\\ & CH=DK \\\\ \\end{align} \\right.$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow \\Delta ACH = \\Delta BDK$ (c\u1ea1nh huy\u1ec1n_c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow AH=BK$ ( hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> D\u1ec5 d\u00e0ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c t\u1ee9 gi\u00e1c $CDKH$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt <br\/> N\u00ean $CD=HK$ <br\/> T\u1eeb \u0111\u00f3 $AH = BK=\\dfrac{AB-HK}{2}=\\dfrac{AB-CD}{2}=\\dfrac{25-7}{2}=9 \\,\\,\\left( cm \\right)$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $9$ <\/span><\/span> "}]}],"id_ques":1458},{"time":24,"part":[{"time":3,"title":"Cho tam gi\u00e1c $ABC.$ Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $AB$ l\u1ea5y m\u1ed9t \u0111i\u1ec3m $D$ sao cho $AD=AC.$ V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $DBC.$ T\u1eeb $O$ l\u1ea7n l\u01b0\u1ee3t h\u1ea1 c\u00e1c \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c $OH, \\,OK$ v\u1edbi $BC$ v\u00e0 $BD$ $\\left( H\\in BC;\\,K\\in BD \\right)$ Ch\u1ee9ng minh $OH >OK$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[4],[3],[1]]],"list":[{"point":5,"left":["M\u00e0 $AD=AC$ (gi\u1ea3 thi\u1ebft)","Trong \u0111\u01b0\u1eddng tr\u00f2n $(O)$ c\u00f3 $BC< BD \\Rightarrow OH > OK$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y)","N\u00ean $BC < AB + AD$ hay $BC < BD$ ","X\u00e9t $\\Delta ABC$ c\u00f3: $BC < AB +AC$ (b\u1ea5t \u0111\u1eb3ng th\u1ee9c trong tam gi\u00e1c) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D19.png' \/><\/center> <br\/> X\u00e9t $\\Delta ABC$ c\u00f3: $BC < AB +AC$ (b\u1ea5t \u0111\u1eb3ng th\u1ee9c trong tam gi\u00e1c) <br\/> M\u00e0 $AD=AC$ (gi\u1ea3 thi\u1ebft) <br\/> N\u00ean $BC < AB + AD$ hay $BC < BD$ <br\/> Trong \u0111\u01b0\u1eddng tr\u00f2n $(O)$ c\u00f3 $BC < BD \\Rightarrow OH > OK$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <\/span>"}]}],"id_ques":1459},{"time":24,"part":[{"time":3,"title":"Trong \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ cho d\u00e2y $AB$ v\u00e0 \u0111\u01b0\u1eddng k\u00ednh $MN.$ Bi\u1ebft $MN \\bot AB.$ Ch\u1ee9ng minh $\\overset\\frown{MA}=\\overset\\frown{MB}$ ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[4],[1],[3]]],"list":[{"point":5,"left":["Ta c\u00f3: $MN\\bot AB \\Rightarrow IA=IB$ (\u0111\u1ecbnh l\u00fd li\u00ean h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung)","Do \u0111\u00f3 $\\overset\\frown{MA}=\\overset\\frown{MB}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y)","G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $MN$ v\u00e0 $AB$ ","M\u00e0 $OA=OB=R$ $\\Rightarrow OM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> Suy ra $MA=MB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv1/img\/h932_D20.png' \/><\/center> <br\/> G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $MN$ v\u00e0 $AB$ <br\/> Ta c\u00f3: $MN\\bot AB $ <br\/> $\\Rightarrow IA=IB$ (\u0111\u1ecbnh l\u00fd li\u00ean h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> M\u00e0 $OA=OB=R$ <br\/> $\\Rightarrow OM$ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> Suy ra $MA=MB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c) <br\/> Do \u0111\u00f3 $\\overset\\frown{MA}=\\overset\\frown{MB}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <\/span>"}]}],"id_ques":1460}],"lesson":{"save":0,"level":1}}