{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["90"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ Tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $O$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $\\widehat{CAB}=30^o$. Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $BA$ l\u1ea5y \u0111i\u1ec3m $M$ sao cho $BM = R$ <br\/><b> C\u00e2u 1: <\/b> $\\widehat{OCM}=$_input_$^o$<\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K7.jpg' \/><\/center><span class='basic_left'> $\\Delta ABC$ c\u00f3: $ OC =\\dfrac{AB}{2}= R$ <br\/> $\\Rightarrow \\Delta ABC$ vu\u00f4ng t\u1ea1i $C$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{CBA}+\\widehat{CAB}=90^o\\\\ \\Rightarrow \\widehat{CBA}=90^o-30^o=60^o$ <br\/> $\\Delta OCB$ c\u00f3: <br\/> $OC = OB = R $<br\/> $\\widehat{CBA}=60^o$ <br\/> Suy ra $\\Delta OBC $ \u0111\u1ec1u <br\/> $\\Rightarrow BC = R$ <br\/> $\\Delta OCM $ c\u00f3: $BC=\\dfrac{OM}{2} = R$ <br\/> Suy ra $\\Delta OCM$ vu\u00f4ng t\u1ea1i $C$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{OCM}=90^o$<br\/><span class='basic_pink'>K\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $90.$<\/span><\/span>"}]}],"id_ques":1171},{"time":9,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $2\\sqrt{3}$","B. $5\\sqrt{3}$","C. $\\sqrt{3}$"],"ques":"<span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ Tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $O$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $\\widehat{CAB}=30^o$. Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $BA$ l\u1ea5y \u0111i\u1ec3m $M$ sao cho $BM = R$ <br\/><b> C\u00e2u 2: <\/b> V\u1edbi $R = 2,$ \u0111\u1ed9 d\u00e0i c\u1ea1nh $MC$ l\u00e0 ?<\/span>","hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pitago","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K7.jpg' \/><\/center> <span class='basic_left'> $\\Delta OCM$ c\u00f3: $\\widehat{C}=90^o$ (theo c\u00e2u 1) <br\/> $\\Rightarrow OC^2 + CM^2=OM^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow CM^2=OM^2-OC^2$ <br\/> $ \\Rightarrow CM^2=4^2-2^2=12\\\\ \\Rightarrow CM =2\\sqrt{3}$ "}]}],"id_ques":1172},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["1"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> H\u00ecnh thang $ABCD$ c\u00f3 $\\widehat{A}=\\widehat{D}=90^o$ c\u00f3 $AB =1; AD=CD= 4.$ V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC.$ \u0110\u01b0\u1eddng th\u1eb3ng $AD$ giao \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$ t\u1ea1i bao nhi\u00eau \u0111i\u1ec3m? <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> _input_ \u0111i\u1ec3m<\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K6.jpg' \/><\/center><span class='basic_left'> V\u1ebd $BH \\bot CD$ t\u1ea1i $H$ <br\/> $\\Rightarrow$ T\u1ee9 gi\u00e1c $ABHD$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt <br\/> $\\Rightarrow BH = AD = 4;$ $ DH= $AB$ =1$ <br\/> Suy ra $HC = CD - CH = 4 - 1 = 3$ <br\/> X\u00e9t $\\Delta BHC$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $BC^2=HC^2+HB^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow BC = \\sqrt{HC^2+HB^2}$ <br\/> $= \\sqrt{3^2+4^2}= 5$ <br\/> Do \u0111\u00f3 $R=\\dfrac{BC}{2} = 2, 5 $ <br\/> V\u1ebd $OM \\bot AD$ <br\/> $\\Rightarrow AB \/\/ OM \/\/ DC$ (v\u00ec c\u00f9ng vu\u00f4ng g\u00f3c $ AD$) <br\/> M\u00e0 $OB = OC = R$ <br\/> $\\Rightarrow OM$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang $ABCD$ (\u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang) <br\/> $\\Rightarrow OM =\\dfrac{AB+CD}{2} =\\dfrac{4 + 1}{2} =2,5$ <br\/> $OM$ l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $AD$ <br\/> Do \u0111\u00f3 $d= R= 2, 5$ $\\Rightarrow$ \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng $AD$ ti\u1ebfp x\u00fac nhau<br\/> $\\Rightarrow$ \u0111\u01b0\u1eddng th\u1eb3ng $AD$ giao v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$ t\u1ea1i 1 \u0111i\u1ec3m <br\/><span class='basic_pink'>K\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $1.$<\/span><\/span>"}]}],"id_ques":1173},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u ","temp":"fill_the_blank","correct":[[["OCP"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'> Cho \u0111i\u1ec3m $C$ tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ T\u1eeb $O$ v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi AC c\u1eaft ti\u1ebfp tuy\u1ebfn t\u1ea1i $C$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ t\u1ea1i $P$<br\/><b> C\u00e2u 1:<\/b> Khi \u0111\u00f3, ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c c\u1eb7p tam gi\u00e1c b\u1eb1ng nhau l\u00e0: $\\Delta OBP=\\Delta\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$<\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K5a.jpg' \/><\/center><span class='basic_left'> $\\Delta OAC $ c\u00e2n t\u1ea1i $O$ (v\u00ec $OA = OC = R$) <br\/> $\\Rightarrow \\widehat{A_{1}}=\\widehat{C_{1}}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $AC \/\/ OP$ (gi\u1ea3 thi\u1ebft ) $\\Rightarrow \\widehat{A_{1}}=\\widehat{O_{1}}$ (\u0111\u1ed3ng v\u1ecb) <br\/> $\\widehat{C_{1}}=\\widehat{O_{2}}$ (so le trong) <br\/> Suy ra $\\widehat{O_{1}}=\\widehat{O_{2}}$ <br\/> X\u00e9t $\\Delta OCP$ v\u00e0 $\\Delta OBP$ c\u00f3: <br\/> $OC= OB = R$ <br\/> $\\widehat{O_{1}}=\\widehat{O_{2}}$ <br\/> $OP$ chung <br\/> $\\Rightarrow \\Delta OCP =\\Delta OBP$ (c.g.c) <br\/><span class='basic_pink'> K\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $OCP$ <\/span><\/span>"}]}],"id_ques":1174},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111i\u1ec3m $C$ tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ T\u1eeb $O$ v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi $AC$ c\u1eaft ti\u1ebfp tuy\u1ebfn t\u1ea1i $C$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ t\u1ea1i $P$ <br\/><b> C\u00e2u 2: <\/b> Ch\u1ee9ng minh $PB$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$<\/span>","title_trans":"S\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 c\u00e1c b\u01b0\u1edbc ch\u1ee9ng minh b\u00e0i to\u00e1n ","temp":"sequence","correct":[[[2],[3],[1],[5],[4]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K5a.jpg","left":["$\\Rightarrow \\widehat{OCP}=\\widehat{OBP}=90^o$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng)","Suy ra $OB \\bot BP$ t\u1ea1i $B$","$\\Delta OCP =\\Delta OPB$ (theo c\u00e2u 1) ","Do \u0111\u00f3 $PB$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn)","M\u00e0 $OB = R$"],"top":80,"explain":"<span class='basic_left'> $\\Delta OCP =\\Delta OPB$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\widehat{OCP}=\\widehat{OBP}=90^o$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> Suy ra $OB \\bot BP $ t\u1ea1i $ B$ <br\/> M\u00e0 $OB = R$ <br\/> Do \u0111\u00f3 $PB$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ti\u1ebfp tuy\u1ebfn) <\/span>"}]}],"id_ques":1175},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<span class='basic_left'> Cho tam gi\u00e1c $OBC$ c\u00e2n t\u1ea1i $O;$ $\\widehat{O}=120^o, BC= 6$. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n $(O; \\sqrt{3})$ <br\/>Khi \u0111\u00f3, $BC$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; \\sqrt{3})$ <\/span>","select":["A. \u0110\u00fang","B. Sai"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K4.jpg' \/><\/center><span class='basic_left'> $\\Delta OBC$ c\u00e2n t\u1ea1i $O$; $\\widehat{O}=120^o$$\\Rightarrow \\widehat{B}=\\dfrac{180^o-\\widehat{O}}{2}=30^o$<br\/> V\u1ebd $OH \\bot BC$ <br\/> $\\Rightarrow BH = HC =3$ <br\/> X\u00e9t $\\Delta OBH $ c\u00f3 $\\widehat{H}=90^o$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $OBH$ ta c\u00f3: <br\/> $OH=HB.tg B$$=3.tg 30^o=\\sqrt{3}$ <br\/> $OH = \\sqrt{3}$ $\\Rightarrow BC$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; \\sqrt{3})$ <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00fang<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1176},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $DEF$ c\u00e2n t\u1ea1i $D$ v\u00e0 n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $O.$ Ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$ l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng<\/span>","select":["A. \u0110i qua $D$ v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi $DE$ ","B. \u0110i qua $D$ v\u00e0 song song v\u1edbi $EF$ ","C. \u0110i qua $D$ v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi $DF$ ","D. \u0110i qua $D$ v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi $EF$ "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K3.jpg' \/><\/center><span class='basic_left'> Ta c\u00f3 $DE = DF$ ($\\Delta DEF$ c\u00e2n t\u1ea1i $D$)<br\/> $OE = OF = R$ <br\/> $\\Rightarrow OD $ l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $EF$ <br\/> Do \u0111\u00f3: $OD \\bot EF$ (1) <br\/> G\u1ecdi $xy$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ t\u1ea1i $D$ <br\/> $ \\Rightarrow xy \\bot OD$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow EF \/\/ xy$ (t\u1eeb vu\u00f4ng g\u00f3c t\u1edbi song song) <br\/> Do \u0111\u00f3 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$ l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua $D$ v\u00e0 song song v\u1edbi $EF$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":1177},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $O,$ \u0111\u01b0\u1eddng k\u00ednh $AB=2R.$ K\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $A,$ \u0111\u01b0\u1eddng th\u1eb3ng $d_{2}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B.$ Tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ l\u1ea5y \u0111i\u1ec3m $C$ (kh\u00e1c $A$). \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $CO$ c\u1eaft $d_{2}$ t\u1ea1i D<br\/><b> C\u00e2u 1: <\/b> X\u00e9t v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng $CD$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n $(O)$ <\/span>","select":["<span class='basic_left'>A. \u0110\u01b0\u1eddng th\u1eb3ng $CD$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O)$ c\u1eaft nhau<\/span>","<span class='basic_left'>B. \u0110\u01b0\u1eddng th\u1eb3ng $CD$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O)$ ti\u1ebfp x\u00fac nhau<\/span>","<span class='basic_left'>C. \u0110\u01b0\u1eddng th\u1eb3ng $CD$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O)$ kh\u00f4ng giao<\/span>"],"hint":"K\u1ebb $OH \\bot CD$ t\u1ea1i $H,$ k\u00e9o d\u00e0i $CO$ c\u1eaft $d_{2}$ t\u1ea1i $E.$ ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K1.jpg' \/><\/center><span class='basic_left'> K\u1ebb $OH \\bot CD$ t\u1ea1i $H,$ k\u00e9o d\u00e0i $CO$ c\u1eaft $d_{2}$ t\u1ea1i $E.$ <br\/> X\u00e9t $\\Delta AOC$ v\u00e0 $\\Delta BOE$ c\u00f3:<br\/> $OA = OB = R$ <br\/> $\\widehat{A}=\\widehat{B}=90^o$ <br\/> $\\widehat{AOC}=\\widehat{BOE}$ (hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh) <br\/> $\\Rightarrow\\Delta AOC =\\Delta BOE\\,(c.g.c)$ <br\/> $\\Rightarrow OC = OE$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> X\u00e9t $\\Delta OCD$ v\u00e0 $\\Delta ODE$ c\u00f3: <br\/> $\\widehat{DOC}=\\widehat{DOE}=90^o$ <br\/> $OC =OE$ (ch\u1ee9ng minh tr\u00ean) <br\/> $OD$ chung <br\/> $\\Rightarrow\\Delta DOC =\\Delta DOE\\,(g.c.g)$ <br\/> Suy ra $\\widehat{D_{1}}=\\widehat{D_{2}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng ) <br\/> $\\Rightarrow OH = OB$ (t\u00ednh ch\u1ea5t tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c) <br\/> Do \u0111\u00f3 $CD$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O)$ ti\u1ebfp x\u00fac nhau <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":1}]}],"id_ques":1178},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $O,$ \u0111\u01b0\u1eddng k\u00ednh $AB=2R.$ K\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $A,$ \u0111\u01b0\u1eddng th\u1eb3ng $d_{2}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B.$ Tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ l\u1ea5y \u0111i\u1ec3m $C$ (kh\u00e1c A). \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $CO$ c\u1eaft $d_{2}$ t\u1ea1i $D.$ <br\/><b> C\u00e2u 2: <\/b> \u0110i\u1ec3m $C$ \u1edf v\u1ecb tr\u00ed n\u00e0o th\u00ec t\u1ed5ng $AC + BD$ nh\u1ecf nh\u1ea5t<\/span>","select":["A. $AC= R$","B. $AC= R\\sqrt{2}$","C. $AC= R\\sqrt{3}$","D. $AC= 2R$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K2.jpg' \/><\/center><span class='basic_left'> K\u1ebb $DK \\bot d_{1}$. <br\/> T\u1ee9 gi\u00e1c $ABDK$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt $\\Rightarrow KD=AB$ <br\/> D\u1ec5 th\u1ea5y $\\Delta AOC =\\Delta HOC$ (c\u1ea1nh huy\u1ec1n-c\u1ea1nh g\u00f3c vu\u00f4ng) $\\Rightarrow AC= HC$ <br\/>V\u00e0 $\\Delta BOD =\\Delta HOD$ (c\u1ea1nh huy\u1ec1n-c\u1ea1nh g\u00f3c vu\u00f4ng ) $\\Rightarrow BD= HD$ <br\/> Suy ra $AC + BD= HC + HD = CD$ <br\/>X\u00e9t $\\Delta KCD$ c\u00f3: $ \\widehat{K}=90^o$ $\\Rightarrow CD \\ge KD = AB$ <br\/> Do \u0111\u00f3 $AC + BD \\ge AB$ <br\/> V\u00ec v\u1eady $(AC + BD) _{min}$ khi $CD = AB$ <br\/>$\\Leftrightarrow CD \/\/AB$$ \\Leftrightarrow AC= OH=\\dfrac{AB}{2}=R$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":4}]}],"id_ques":1179},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["9"]]],"list":[{"point":10,"width":50,"content":"","type_input":"","ques":"<span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $O,$ \u0111\u01b0\u1eddng k\u00ednh $AB=2R.$ K\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $A,$ \u0111\u01b0\u1eddng th\u1eb3ng $d_{2}$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $B.$ Tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng $d_{1}$ l\u1ea5y \u0111i\u1ec3m $C$ (kh\u00e1c A). \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $CO$ c\u1eaft $d_{2}$ t\u1ea1i $D.$ <br\/><b> C\u00e2u 3: <\/b> Cho $AB = 6 .$ T\u00edch $AC.BD$ l\u00e0 _input_<\/span>","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng $h^2=b'.c'$","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai8/lv3/img\/H923_K2.jpg' \/><\/center><span class='basic_left'> Ta c\u00f3 $AC = HC, BD = HD$ (theo c\u00e2u 2) <br\/> Do \u0111\u00f3: $AC.BD=HC.HD$ <br\/> $\\Delta COD$ c\u00f3: $\\widehat{O}=90^o$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng $COD$ ta c\u00f3: <br\/> $HC.HD=OH^2$ <br\/>$\\Rightarrow HC.HD=3^2=9$<br\/> Suy ra $AC.BD=9$ <br\/><span class='basic_pink'>K\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $9.$ <\/span><\/span>"}]}],"id_ques":1180}],"lesson":{"save":0,"level":3}}