{"segment":[{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"G\u00f3c n\u1ed9i ti\u1ebfp l\u00e0 g\u00f3c c\u00f3: ","select":["A. \u0110\u1ec9nh n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 hai c\u1ea1nh ch\u1ee9a hai d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 ","B. \u0110\u1ec9nh n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 hai c\u1ea1nh ch\u1ee9a hai d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 ","C. \u0110\u1ec9nh n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 hai c\u1ea1nh ch\u1ee9a hai d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 ","D. \u0110\u1ec9nh n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 lu\u00f4n nh\u1ecf h\u01a1n $180^o$"],"explain":" Theo \u0111\u1ecbnh ngh\u0129a g\u00f3c n\u1ed9i ti\u1ebfp th\u00ec <br\/> G\u00f3c n\u1ed9i ti\u1ebfp l\u00e0 g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 hai c\u1ea1nh ch\u1ee9a hai d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span><\/span>","column":1}]}],"id_ques":1471},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" H\u00ecnh v\u1ebd n\u00e0o trong c\u00e1c h\u00ecnh v\u1ebd sau bi\u1ec3u di\u1ec5n g\u00f3c n\u1ed9i ti\u1ebfp?","select":["A. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D2.1.png' \/><\/center> ","B. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D2.2.png' \/><\/center> ","C. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D2.3.png' \/><\/center> ","D. <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D2.4.png' \/><\/center>"],"explain":"<span class='basic_left'> \u0110\u00e1p \u00e1n A g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n $\\Rightarrow$ Lo\u1ea1i <br\/> \u0110\u00e1p \u00e1n B th\u1ecfa m\u00e3n \u0111\u1ecbnh ngh\u0129a g\u00f3c n\u1ed9i ti\u1ebfp<br\/> \u0110\u00e1p \u00e1n C g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $\\Rightarrow$ Lo\u1ea1i <br\/> \u0110\u00e1p \u00e1n D g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n nh\u01b0ng m\u1ed9t c\u1ea1nh ch\u1ee9a d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u00f2n m\u1ed9t c\u1ea1nh th\u00ec kh\u00f4ng $\\Rightarrow$ Lo\u1ea1i <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":2}]}],"id_ques":1472},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung th\u00ec b\u1eb1ng nhau.","select":["A. \u0110\u00fang ","B. Sai "],"explain":"<span class='basic_left'> Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, g\u00f3c n\u1ed9i ti\u1ebfp b\u1eb1ng n\u1eeda s\u1ed1 \u0111o c\u1ee7a cung b\u1ecb ch\u1eafn (\u0111\u1ecbnh l\u00ed) <br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung b\u1eb1ng n\u1eeda s\u1ed1 \u0111o c\u1ee7a cung b\u1ecb ch\u1eafn (\u0111\u1ecbnh l\u00ed) <br\/> Suy ra kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0111\u00fang <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span><\/span>","column":2}]}],"id_ques":1473},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["45"],["68"],["60"],["120"]]],"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/bai15/lv1/img\/h933_D4.png' \/><\/center> <br\/> H\u00e3y ho\u00e0n th\u00e0nh b\u1ea3ng sau: <br\/> <table><tr><td>S\u1ed1 \u0111o $\\widehat{BAx}$<\/td><td>$30^o$<\/td><td>_input_$^o$<\/td><td>_input_$^o$<\/td><td>$60^o$<\/td><\/tr><tr><td>S\u1ed1 \u0111o $\\overset\\frown{AmB}$<\/td><td>_input_$^o$<\/td><td>$90^o$<\/td><td>$136^o$<\/td><td>_input_$^o$<\/td><\/tr><\/table>","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D4.png' \/><\/center> <br\/> S\u1ed1 \u0111o c\u1ee7a g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung b\u1eb1ng n\u1eeda s\u1ed1 \u0111o c\u1ee7a cung b\u1ecb ch\u1eafn (\u0111\u1ecbnh l\u00ed) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AmB}=2\\widehat{BAx}$ <br\/> V\u1eady ta c\u00f3 b\u1ea3ng <br\/> <table><tr><td>S\u1ed1 \u0111o $\\widehat{BAx}$<\/td><td>$30^o$<\/td><td>$45^o$<\/td><td>$68^o$<\/td><td>$60^o$<\/td><\/tr><tr><td>S\u1ed1 \u0111o $\\overset\\frown{AmB}$<\/td><td>$60^o$<\/td><td>$90^o$<\/td><td>$136^o$<\/td><td>$120^o$<\/td><\/tr><\/table> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $45,\\, 68,\\, 60$ v\u00e0 $120$ <\/span><\/span> "}]}],"id_ques":1474},{"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 $\\left( O \\right)$, $\\widehat{A}={{40}^{o}}.$ S\u1ed1 \u0111o c\u1ee7a g\u00f3c $BOC$ b\u1eb1ng: ","select":["A. ${{40}^{o}}$ ","B. ${{80}^{o}}$ ","C. ${{140}^{o}}$ ","D. ${{110}^{o}}$ "],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D5.png' \/><\/center> <br\/> G\u00f3c n\u1ed9i ti\u1ebfp (nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng $90^o$) c\u00f3 s\u1ed1 \u0111o b\u1eb1ng n\u1eeda s\u1ed1 \u0111o c\u1ee7a g\u00f3c \u1edf t\u00e2m c\u00f9ng ch\u1eafn m\u1ed9t cung (h\u1ec7 qu\u1ea3) <br\/> $\\Rightarrow \\widehat{BOC}= 2\\widehat{BAC}$ $=2.40^o=80^o$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":4}]}],"id_ques":1475},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c nh\u1ecdn $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $\\left( O \\right)$, \u0111\u01b0\u1eddng cao $AH$. K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $AE$. Ch\u1ee9ng minh r\u1eb1ng $\\widehat{BAH}=\\widehat{OAC}.$","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],[5]]],"list":[{"point":5,"left":["X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta AHB$ v\u00e0 $\\Delta ACE$ c\u00f3:","M\u00e0 $\\widehat{ABC}=\\widehat{AEC}$ (ch\u1ee9ng minh tr\u00ean) hay $\\widehat{ABH}=\\widehat{AEC}$","Ta c\u00f3: $\\widehat{ABC}=\\widehat{AEC}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung)<br\/> $\\widehat{ACE}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)","$\\widehat{BAH}+\\widehat{ABH}=\\widehat{CAE}+\\widehat{AEC}={{90}^{o}}$ ","$\\Rightarrow \\widehat{BAH}=\\widehat{CAE}$ (c\u00f9ng ph\u1ee5 v\u1edbi hai g\u00f3c b\u1eb1ng nhau)"],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D6.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{ABC}=\\widehat{AEC}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $AC$) <br\/> $\\widehat{ACE}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta AHB$ v\u00e0 $\\Delta ACE$ c\u00f3: <br\/> $\\widehat{BAH}+\\widehat{ABH}=\\widehat{CAE}+\\widehat{AEC}={{90}^{o}}$ <br\/> M\u00e0 $\\widehat{ABC}=\\widehat{AEC}$ (ch\u1ee9ng minh tr\u00ean) <br\/> Hay $\\widehat{ABH}=\\widehat{AEC}$ <br\/> $\\Rightarrow \\widehat{BAH}=\\widehat{CAE}$ (c\u00f9ng ph\u1ee5 v\u1edbi hai g\u00f3c b\u1eb1ng nhau) <\/span>"}]}],"id_ques":1476},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'> Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $\\left( O;R \\right)$, \u0111\u01b0\u1eddng k\u00ednh $AB, K$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa cung $AB$. V\u1ebd b\u00e1n k\u00ednh $OC$ sao cho $\\widehat{BOC}={{60}^{o}}.$ G\u1ecdi $M$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AC$ v\u00e0 $OK$. \u0110\u1ed9 d\u00e0i $OM$ l\u00e0:","select":["A. $\\dfrac{R}{2}$ ","B. $\\dfrac{R\\sqrt{2}}{2}$ ","C. $\\dfrac{R\\sqrt{3}}{3}$ ","D. $\\dfrac{R}{3}$"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D7.png' \/><\/center><br\/> Ta c\u00f3: $\\widehat{BOC}={{60}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{CAB}=\\dfrac{1}{2}\\widehat{BOC}=\\dfrac{1}{2}{{.60}^{o}}={{30}^{o}}$ (h\u1ec7 qu\u1ea3 c\u1ee7a g\u00f3c n\u1ed9i ti\u1ebfp) <br\/> Do $K$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa cung $AB$ <br\/> $\\Rightarrow OK\\bot AB$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> X\u00e9t $\\Delta AMO$ vu\u00f4ng t\u1ea1i $O$ c\u00f3: <br\/> $OM=OA.tg \\widehat{MAO}$ (t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow OM=OA.tg {{30}^{o}}=\\dfrac{R\\sqrt{3}}{3}$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C <\/span><\/span>","column":4}]}],"id_ques":1477},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c nh\u1ecdn $ABC$. \u0110\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $BC$ c\u1eaft $AB, AC$ theo th\u1ee9 t\u1ef1 \u1edf $D$ v\u00e0 $E$. G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $BE$ v\u00e0 $CD$. <br\/> <b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh r\u1eb1ng $AI$ vu\u00f4ng g\u00f3c v\u1edbi $BC$","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":[" $\\Rightarrow BE\\bot AC;CD\\bot AB$","$\\Rightarrow AI\\bot BC$ ","Ta c\u00f3: $\\widehat{BDC}=\\widehat{BEC}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)","$\\Rightarrow I$ l\u00e0 tr\u1ef1c t\u00e2m tam gi\u00e1c $ABC$ "],"top":55,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D9.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{BDC}=\\widehat{BEC}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)<br\/> $\\Rightarrow BE\\bot AC;CD\\bot AB$ <br\/> $\\Rightarrow I$ l\u00e0 tr\u1ef1c t\u00e2m tam gi\u00e1c $ABC$ <br\/> $\\Rightarrow AI\\bot BC$ <\/span>"}]}],"id_ques":1478},{"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 nh\u1ecdn $ABC$. \u0110\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $BC$ c\u1eaft $AB, AC$ theo th\u1ee9 t\u1ef1 \u1edf $D$ v\u00e0 $E$. G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $BE$ v\u00e0 $CD$. <br\/> <b> C\u00e2u 2:<\/b> So s\u00e1nh $\\widehat{IDE}$ v\u00e0 $\\widehat{IAE}$ <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b> $\\widehat{IDE}$ _input_ $\\widehat{IAE}$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D10.png' \/><\/center> <br\/> G\u1ecdi $K$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AI$ v\u00e0 $BC\\Rightarrow \\widehat{AKC}=90^o$ (t\u00ednh ch\u1ea5t tr\u1ef1c t\u00e2m) <br\/> Ta c\u00f3: $\\widehat{EDC}=\\widehat{EBC}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) <br\/> $\\widehat{EBC}=\\widehat{KAC}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{ECB}$) <br\/> $\\Rightarrow \\widehat{EDC}=\\widehat{KAC}$ Hay $\\widehat{IDE}=\\widehat{IAE}$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$<\/span> <\/span> "}]}],"id_ques":1479},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $\\left( O \\right)$, \u0111\u01b0\u1eddng k\u00ednh $AB$, \u0111i\u1ec3m $D$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n. G\u1ecdi $E$ l\u00e0 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi $A$ qua $D, K$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $EB$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n. Ch\u1ee9ng minh $OD$ vu\u00f4ng g\u00f3c v\u1edbi $AK.$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[7],[2],[5],[3],[6],[1]]],"list":[{"point":5,"left":[" $\\Rightarrow \\widehat{ABD}=\\widehat{EBD}$ (t\u00ednh ch\u1ea5t ph\u00e2n gi\u00e1c)","T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{DAK}+\\widehat{ADO}=\\widehat{DAB}+\\widehat{DBA}={{90}^{o}}$ <br\/> $\\Rightarrow \\Delta ADI$ vu\u00f4ng t\u1ea1i $I\\Rightarrow AK\\bot OD$","X\u00e9t $\\Delta ABE$ c\u00f3: $\\left\\{ \\begin{align} & AD\\bot BD\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & AD=DE\\left( \\text{gi\u1ea3 thi\u1ebft} \\right) \\\\ \\end{align} \\right.$"," M\u00e0 $\\widehat{DAK}=\\widehat{DBK}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) $\\Rightarrow \\widehat{DAK}=\\widehat{ABD}\\,(1)$","$\\Rightarrow \\Delta ABE$ c\u00e2n t\u1ea1i $B$ (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow BD$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{ABE}$ ","D\u1ec5 th\u1ea5y $\\Delta OAD$ c\u00e2n t\u1ea1i $O$ $\\Rightarrow \\widehat{ADO}=\\widehat{DAO}\\,(2)$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n)","Ta c\u00f3: $\\widehat{ADB}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow AD\\bot BD$ "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D8.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{ADB}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow AD\\bot BD$ <br\/> X\u00e9t $\\Delta ABE$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & AD\\bot BD\\left( \\text{Ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & AD=DE\\left( \\text{gi\u1ea3 thi\u1ebft} \\right) \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta ABE$ c\u00e2n t\u1ea1i $B$ (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow BD$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $\\widehat{ABE}$ <br\/> $\\Rightarrow \\widehat{ABD}=\\widehat{EBD}$ (t\u00ednh ch\u1ea5t ph\u00e2n gi\u00e1c) <br\/> M\u00e0 $\\widehat{DAK}=\\widehat{DBK}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) <br\/> $\\Rightarrow \\widehat{DAK}=\\widehat{ABD}\\,(1)$ <br\/> D\u1ec5 th\u1ea5y $\\Delta OAD$ c\u00e2n t\u1ea1i $O$ <br\/> $\\Rightarrow \\widehat{ADO}=\\widehat{DAO}\\,(2)$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{DAK}+\\widehat{ADO}=\\widehat{DAB}+\\widehat{DBA}={{90}^{o}}$ <br\/> $\\Rightarrow \\Delta ADI$ vu\u00f4ng t\u1ea1i $I\\Rightarrow AK\\bot OD$ <\/span>"}]}],"id_ques":1480},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["30"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D11.png' \/><\/center> <br\/> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O;R)$, d\u00e2y cung $AB$ c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng b\u00e1n k\u00ednh $R$. K\u1ebb ti\u1ebfp tuy\u1ebfn $Bx$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$. S\u1ed1 \u0111o g\u00f3c $\\widehat{xBA}$ l\u00e0 _input_ $^o$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D11.png' \/><\/center> <br\/> X\u00e9t $\\Delta OAB$ c\u00f3: <br\/> $OA= OB = AB=R$ <br\/> $\\Rightarrow \\Delta OAB$ \u0111\u1ec1u (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c \u0111\u1ec1u) <br\/> $\\Rightarrow \\widehat{AOB} = 60^o$ (t\u00ednh ch\u1ea5t tam gi\u00e1c \u0111\u1ec1u) <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AB} = 60^o$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow \\widehat{ABx} = \\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{AB}=\\dfrac{1}{2}.60^o=30^o$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $30$ <\/span><\/span> "}]}],"id_ques":1481},{"time":24,"part":[{"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$, d\u00e2y cung $MN,$ ti\u1ebfp tuy\u1ebfn $Mx$. Tr\u00ean $Mx$ l\u1ea5y \u0111i\u1ec3m $T$, $TN$ c\u1eaft $(O)$ t\u1ea1i $S$. ","title_trans":"C\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","temp":"true_false","correct":[["t","t","f","t"]],"list":[{"point":5,"col_name":["","\u0110\u00fang","Sai"],"arr_ques":[" $\\widehat{TSM} = \\widehat{TMN}$ ","$\\Delta TMN$ v\u00e0 $\\Delta TSM$ \u0111\u1ed3ng d\u1ea1ng","$\\dfrac{TM}{TS}=\\dfrac{TN}{SM}$","$TM^2=TN.TS$ "],"explain":["<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D12.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{TSM} = \\widehat{TMN}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $MN$) <br\/> $\\Rightarrow$ Kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang.","<br\/><span class='basic_left'> X\u00e9t $\\Delta TMN$ v\u00e0 $\\Delta TSM$ c\u00f3: <br\/> $\\widehat{TSM} = \\widehat{TMN}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\widehat{T}$ chung <br\/> $\\Rightarrow \\Delta TMN \\backsim \\Delta TSM$ (g.g) <br\/> $\\Rightarrow$ Kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang.","<br\/><span class='basic_left'> $ \\Delta TMN \\backsim \\Delta TSM$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow \\dfrac{TM}{TS}=\\dfrac{TN}{TM}$ (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) <br\/> $\\Rightarrow$ Kh\u1eb3ng \u0111\u1ecbnh sai.","<br\/> <span class='basic_left'> $ \\dfrac{TM}{TS}=\\dfrac{TN}{TM}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\Rightarrow TM^2=TN.TS$ <br\/> $\\Rightarrow$ Kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang."]}]}],"id_ques":1482},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" Cho \u0111\u01b0\u1eddng tr\u00f2n $(O;R),$ \u0111\u01b0\u1eddng k\u00ednh $AB$. Tr\u00ean n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 b\u1edd l\u00e0 $AB$, l\u1ea5y hai \u0111i\u1ec3m $C$ v\u00e0 $D$ sao cho $\\overset\\frown{AC} = \\overset\\frown{CD} = \\overset\\frown{DB}$. Hai ti\u1ebfp tuy\u1ebfn t\u1eeb $C$ v\u00e0 $D$ c\u1eaft nhau t\u1ea1i $E$. S\u1ed1 \u0111o g\u00f3c $\\widehat{CED}$ b\u1eb1ng:","select":["A. ${{30}^{o}}$ ","B. ${{60}^{o}}$ ","C. ${{90}^{o}}$ ","D. ${{120}^{o}}$ "],"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D13.png' \/><\/center> <br\/> Ta c\u00f3: $\\overset\\frown{AC} = \\overset\\frown{CD} = \\overset\\frown{DB}$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{CD} = \\dfrac{\\text{s\u0111}\\overset\\frown{AB}}{3}=\\dfrac{180^o}{3}=60^o$ <br\/> $\\Rightarrow \\widehat{CDE}=\\widehat{DCE} = 30^o$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung ch\u1eafn cung $60^o$) <br\/> M\u00e0 $\\widehat{CDE}+\\widehat{DCE} +\\widehat{CED}= 180^o$ (t\u1ed5ng ba g\u00f3c c\u1ee7a tam gi\u00e1c) <br\/> $\\Rightarrow \\widehat{CED} = 180^o - \\widehat{CDE} - \\widehat{DCE}$ $= 180^o - 30^o-30^o = 120^o$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span><\/span>","column":4}]}],"id_ques":1483},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Hai b\u00e1n k\u00ednh $OA$ v\u00e0 $OB$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ t\u1ea1o th\u00e0nh g\u00f3c $\\widehat{AOB}=55^o$. S\u1ed1 \u0111o c\u1ee7a g\u00f3c t\u00f9 t\u1ea1o b\u1edfi hai ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ v\u00e0 $B$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n l\u00e0:","select":["A. ${{115}^{o}}$ ","B. ${{135}^{o}}$ ","C. ${{125}^{o}}$ ","D. ${{105}^{o}}$ "],"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D14.png' \/><\/center> <br\/> G\u1ecdi $M$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $Ax$ v\u00e0 $By$ <br\/> Ta c\u00f3 $\\widehat{AOB}=55^o$$\\Rightarrow \\text{s\u0111}\\overset\\frown{AB}=55^o$ (\u0111\u1ecbnh ngh\u0129a s\u1ed1 \u0111o cung) <br\/> $\\Rightarrow \\widehat{MAB}=\\widehat{MBA} = \\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{AB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung ch\u1eafn $\\overset\\frown{AB}$) <br\/> $\\Rightarrow \\widehat{MAB}+\\widehat{MBA} =\\text{s\u0111}\\overset\\frown{AB} = 55^o$ <br\/> M\u00e0 $\\widehat{MAB}+\\widehat{MBA} +\\widehat{AMB} = 180^o$ (t\u1ed5ng ba g\u00f3c c\u1ee7a tam gi\u00e1c) <br\/> $\\Rightarrow \\widehat{AMB} = 180^o - (\\widehat{MAB}+\\widehat{MBA}) = 180^o-55^o = 125^o$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C <\/span><\/span>","column":4}]}],"id_ques":1484},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" T\u00ecm g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung trong c\u00e1c h\u00ecnh v\u1ebd sau. <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D15.png' \/><\/center>","select":["A. H\u00ecnh 1 ","B. H\u00ecnh 2 ","C. H\u00ecnh 3 ","D. H\u00ecnh 4 "],"explain":"<span class='basic_left'> \u0110\u00e1p \u00e1n A th\u1ecfa m\u00e3n \u0111\u1ecbnh ngh\u0129a g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung <br\/> \u0110\u00e1p \u00e1n B sai do \u0111\u1ec9nh $A$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n, kh\u00f4ng l\u00e0 ti\u1ebfp \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n <br\/> \u0110\u00e1p \u00e1n C sai do $A$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 kh\u00f4ng c\u00f3 c\u1ea1nh n\u00e0o l\u00e0 d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n <br\/> \u0110\u00e1p \u00e1n $D$ sai do kh\u00f4ng c\u00f3 c\u1ea1nh n\u00e0o l\u00e0 tia ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A <\/span><\/span>","column":4}]}],"id_ques":1485},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho h\u00ecnh v\u1ebd sau: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D16.png' \/><\/center> <br\/> \u0110\u1eb3ng th\u1ee9c n\u00e0o sau \u0111\u00e2y kh\u00f4ng \u0111\u00fang?","select":["A. $\\widehat{ABx} = \\widehat{ACB}$ ","B. $\\widehat{AOB} = \\widehat{ACB}$ ","C. $\\widehat{AOB} = 2 \\widehat{ACB}$ ","D. $\\widehat{AOB} = 2\\widehat{ABx}$ "],"explain":"<span class='basic_left'> <br\/> Ta c\u00f3: $\\widehat{ABx} = \\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{AB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung ch\u1eafn $\\overset\\frown{AB}$) <br\/> $\\widehat{ACB} = \\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{AB}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn $\\overset\\frown{AB}$) <br\/> $\\widehat{AOB} = \\text{s\u0111}\\overset\\frown{AB}$ (g\u00f3c \u1edf t\u00e2m ch\u1eafn $\\overset\\frown{AB}$) <br\/> $\\Rightarrow \\widehat{ABx} = \\widehat{ACB}; \\,\\widehat{AOB} = 2 \\widehat{ACB}; \\, \\widehat{AOB} = 2\\widehat{ABx}$ <br\/> Suy ra \u0111\u00e1p \u00e1n B kh\u00f4ng \u0111\u00fang. <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":4}]}],"id_ques":1486},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["130"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$, hai \u0111i\u1ec3m $A$ v\u00e0 $B$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n. Hai ti\u1ebfp tuy\u1ebfn t\u1ea1i $A, B$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau t\u1ea1i $M$ sao cho $\\widehat{AMB} = 50^o$. S\u1ed1 \u0111o cung nh\u1ecf $AB$ l\u00e0 _input_ $^o$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D17.png' \/><\/center> <br\/> Ta c\u00f3: $MA=MB$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\Delta AMB$ c\u00e2n t\u1ea1i $M$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{MAB}=\\widehat{MBA} $ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> M\u00e0 $\\widehat{MAB}+\\widehat{MBA} +\\widehat{AMB} = 180^o$ (t\u1ed5ng ba g\u00f3c c\u1ee7a tam gi\u00e1c) <br\/> $\\Rightarrow 2\\widehat{MAB} = 180^o - \\widehat{AMB}= 180^o-50^o = 130^o$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AB}=2\\widehat{MAB} = 130^o$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung ch\u1eafn $\\overset\\frown{AB}$) <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $130$ <\/span><\/span> "}]}],"id_ques":1487},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":" <span class='basic_left'> Cho tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n $(O),$ tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $A$ c\u1eaft $(O)$ t\u1ea1i $M.$ Ti\u1ebfp ti\u1ebfp t\u1ea1i $M$ c\u1ee7a $(O)$ c\u1eaft $AB$ v\u00e0 $AC$ l\u1ea7n l\u01b0\u1ee3t t\u1ea1i $D$ v\u00e0 $E.$ Trong c\u00e1c m\u1ec7nh \u0111\u1ec1 sau, m\u1ec7nh \u0111\u1ec1 n\u00e0o kh\u00f4ng \u0111\u00fang? ","select":["A. $DB.MA = DM.BM$ ","B. $DM^2= DA.DB$ ","C. $DB.AD = DM.MA$ ","D. $DB.BM = DM.MA$ "],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D18.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{BMD}=\\widehat{BAM}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $MB$) <br\/> X\u00e9t $\\Delta BMD$ v\u00e0 $\\Delta MAD$ c\u00f3: <br\/> $\\widehat{BMD}=\\widehat{BAM}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\widehat{D}$ chung <br\/> $\\Rightarrow \\Delta BMD\\backsim \\Delta MAD$ (g.g) <br\/> $\\Rightarrow \\dfrac{BM}{MA}=\\dfrac{MD}{AD}=\\dfrac{BD}{MD}$ (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) <br\/> $\\Rightarrow \\left\\{ \\begin{align} & \\dfrac{BM}{MA}=\\dfrac{MD}{AD} \\\\ & \\dfrac{MD}{AD}=\\dfrac{BD}{MD} \\\\ & \\dfrac{BM}{MA}=\\dfrac{BD}{MD} \\\\ \\end{align} \\right.$$\\Rightarrow \\left\\{ \\begin{align} & BM.AD=MA.MD \\\\ & M{{D}^{2}}=AD.BD \\\\ & BM.MD=MA.BD \\\\ \\end{align} \\right.$<br\/> Suy ra \u0111\u00e1p \u00e1n D kh\u00f4ng \u0111\u00fang <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":1488},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$ v\u00e0 m\u1ed9t \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n. K\u1ebb ti\u1ebfp tuy\u1ebfn $MA$ v\u00e0 c\u00e1t tuy\u1ebfn $MBC.$ Ch\u1ee9ng minh $MA^2= MB.MC.$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[5],[4],[1],[3]]],"list":[{"point":5,"left":["X\u00e9t $\\Delta MAB$ v\u00e0 $\\Delta MCA$ c\u00f3: <br\/> $\\widehat{MCA}=\\widehat{MAB}$ (ch\u1ee9ng minh tr\u00ean), $\\widehat{M}$ chung ","$\\Rightarrow M{{A}^{2}}=MB.MC$ "," $\\Rightarrow \\dfrac{MA}{MC}=\\dfrac{MB}{MA}$ (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) "," Ta c\u00f3: $\\widehat{ACB}=\\widehat{MAB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $AB$)","$\\Rightarrow \\Delta MAB\\backsim \\Delta MCA$ (g.g)"],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D19.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{ACB}=\\widehat{MAB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $AB$) <br\/> X\u00e9t $\\Delta MAB$ v\u00e0 $\\Delta MCA$ c\u00f3: <br\/> $\\widehat{MCA}=\\widehat{MAB}$ (ch\u1ee9ng minh tr\u00ean) <br\/> $\\widehat{M}$ chung <br\/> $\\Rightarrow \\Delta MAB\\backsim \\Delta MCA$ (g.g) <br\/> $\\Rightarrow \\dfrac{MA}{MC}=\\dfrac{MB}{MA}$ (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) <br\/> $\\Rightarrow M{{A}^{2}}=MB.MC$ <\/span>"}]}],"id_ques":1489},{"time":24,"part":[{"time":3,"title":"Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $BC$. \u0110i\u1ec3m $A$ thu\u1ed9c cung $BC$ $(AB < AC)$. Ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng $BC$ \u1edf $I$. G\u1ecdi $H$ l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $A$ tr\u00ean $BC$. Ch\u1ee9ng minh $AB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $IAH$. ","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":["$\\Rightarrow \\widehat{BAH}=\\widehat{ACB}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{HAC}$) ","$\\Rightarrow AB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $IAH$ "," Ta c\u00f3: $\\widehat{IAB}=\\widehat{ACB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung)","$\\Rightarrow \\widehat{IAB}=\\widehat{BAH}$ (c\u00f9ng b\u1eb1ng $\\widehat{ACB}$)","$\\widehat{BAC}=90^o$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)"],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai15/lv1/img\/h933_D20.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{IAB}=\\widehat{ACB}$ (g\u00f3c t\u1ea1o b\u1edfi tia ti\u1ebfp tuy\u1ebfn v\u00e0 d\u00e2y cung v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn cung $AB$) <br\/> $\\widehat{BAC}=90^o$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow \\widehat{BAH}=\\widehat{ACB}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{HAC}$) <br\/> $\\Rightarrow \\widehat{IAB}=\\widehat{BAH}$ (c\u00f9ng b\u1eb1ng $\\widehat{ACB}$) <br\/> $\\Rightarrow AB$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c $IAH$ <\/span>"}]}],"id_ques":1490}],"lesson":{"save":0,"level":1}}