{"segment":[{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $AB$ v\u00e0 $D$ l\u00e0 m\u1ed9t \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n ($D$ kh\u00e1c $A$ v\u00e0 $B$). Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $BA$ l\u1ea5y m\u1ed9t \u0111i\u1ec3m $C$. \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $BC$ t\u1ea1i $C$ c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng $AD$ t\u1ea1i $M$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $MCBD$ n\u1ed9i ti\u1ebfp. ","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":["$\\widehat{BDA}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) ","$\\Rightarrow $ T\u1ee9 gi\u00e1c $BCMD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)"," Ta c\u00f3: $\\widehat{MCB}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft)","$\\Rightarrow \\widehat{BDM}={{90}^{o}}$ (k\u1ec1 b\u00f9 v\u1edbi $\\widehat{BDA}$) $\\Rightarrow \\widehat{MCB}+\\widehat{BDM}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D1.png' \/><\/center> <br\/>Ta c\u00f3: $\\widehat{MCB}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\widehat{BDA}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow \\widehat{BDM}={{90}^{o}}$ (k\u1ec1 b\u00f9 v\u1edbi $\\widehat{BDA}$) <br\/> $\\Rightarrow \\widehat{MCB}+\\widehat{BDM}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$ <br\/> $\\Rightarrow $ T\u1ee9 gi\u00e1c $BCMD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1531},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$. \u0110\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $AO$ t\u1ea1i trung \u0111i\u1ec3m $I$ c\u1ee7a $AO$ c\u1eaft $AC$ t\u1ea1i $M$ v\u00e0 c\u1eaft ti\u1ebfp tuy\u1ebfn t\u1ea1i $C$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $E$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $OCEI$ n\u1ed9i ti\u1ebfp.","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[1],[4],[3]]],"list":[{"point":5,"left":["$\\widehat{EIO}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) ","Ta c\u00f3: $\\widehat{OCE}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn)"," $\\Rightarrow $ T\u1ee9 gi\u00e1c $OCEI$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) ","$\\Rightarrow \\widehat{OCE}+\\widehat{EIO}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D2.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{OCE}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) <br\/> $\\widehat{EIO}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{OCE}+\\widehat{EIO}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$ <br\/> $\\Rightarrow $ T\u1ee9 gi\u00e1c $OCEI$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1532},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho t\u1ee9 gi\u00e1c $ABCD$ n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n $(O)$; $I$ l\u00e0 \u0111i\u1ec3m ch\u00ecnh gi\u1eefa cung $AB$ (kh\u00f4ng ch\u1ee9a $C$ v\u00e0 $D$). $IC, ID$ c\u1eaft $AB$ t\u01b0\u01a1ng \u1ee9ng t\u1ea1i $E$ v\u00e0 $F$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $CDFE$ n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[1],[4],[3]]],"list":[{"point":5,"left":["$\\widehat{AFD}=\\dfrac{\\text{s\u0111}\\overset\\frown{AD}+\\text{s\u0111}\\overset\\frown{BI}}{2}$ (\u0111\u1ecbnh l\u00ed g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n) ","Ta c\u00f3: $\\overset\\frown{AI}=\\overset\\frown{BI}$ (do $I$ n\u1eb1m ch\u00ednh gi\u1eefa cung $AB$ )"," $\\Rightarrow $ T\u1ee9 gi\u00e1c $CEFD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","$\\Rightarrow \\widehat{AFD}=\\dfrac{\\text{s\u0111}\\overset\\frown{AD}+\\text{s\u0111}\\overset\\frown{AI}}{2}=\\dfrac{\\text{s\u0111}\\overset\\frown{DAI}}{2}=\\widehat{DCI}$ (\u0111\u1ecbnh l\u00ed g\u00f3c n\u1ed9i ti\u1ebfp)"],"top":75,"hint":"S\u1eed d\u1ee5ng d\u1ea5u hi\u1ec7u g\u00f3c ngo\u00e0i t\u1ea1i m\u1ed9t \u0111\u1ec9nh b\u1eb1ng g\u00f3c trong c\u1ee7a \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D3.png' \/><\/center> <br\/> Ta c\u00f3: $\\overset\\frown{AI}=\\overset\\frown{BI}$ (do $I$ n\u1eb1m ch\u00ednh gi\u1eefa cung $AB$) <br\/> $\\widehat{AFD}=\\dfrac{\\text{s\u0111}\\overset\\frown{AD}+\\text{s\u0111}\\overset\\frown{BI}}{2}$ (\u0111\u1ecbnh l\u00ed g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow \\widehat{AFD}=\\dfrac{\\text{s\u0111}\\overset\\frown{AD}+\\text{s\u0111}\\overset\\frown{AI}}{2}=\\dfrac{\\text{s\u0111}\\overset\\frown{DAI}}{2}=\\widehat{DCI}$ (\u0111\u1ecbnh l\u00ed g\u00f3c n\u1ed9i ti\u1ebfp) <br\/> $\\Rightarrow $ T\u1ee9 gi\u00e1c $CEFD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1533},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. K\u1ebb $HD$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $D$; $HE$ vu\u00f4ng g\u00f3c v\u1edbi $AC$ t\u1ea1i $E$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $BDEC$ n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[3],[2],[1]]],"list":[{"point":5,"left":["$\\Rightarrow BDEC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) ","M\u1eb7t kh\u00e1c $\\widehat{AHE}=\\widehat{ACH}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{HAC}$) $\\Rightarrow \\widehat{ADE}=\\widehat{ACH}$"," $\\Rightarrow \\widehat{ADE}=\\widehat{AHE}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung)"," D\u1ec5 d\u00e0ng ch\u1ee9ng minh $ADHE$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt $\\Rightarrow ADHE$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D4.png' \/><\/center> <br\/> D\u1ec5 d\u00e0ng ch\u1ee9ng minh $ADHE$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt <br\/> $\\Rightarrow ADHE$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow \\widehat{ADE}=\\widehat{AHE}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) <br\/> M\u1eb7t kh\u00e1c $\\widehat{AHE}=\\widehat{ACH}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{HAC}$) <br\/> $\\Rightarrow \\widehat{ADE}=\\widehat{ACH}$ <br\/> $\\Rightarrow BDEC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1534},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong c\u00e1c h\u00ecnh sau, h\u00ecnh n\u00e0o lu\u00f4n n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n?","select":["A. H\u00ecnh b\u00ecnh h\u00e0nh ","B. H\u00ecnh thang ","C. H\u00ecnh thoi ","D. H\u00ecnh ch\u1eef nh\u1eadt"],"explain":" <span class='basic_left'> H\u00ecnh ch\u1eef nh\u1eadt l\u00e0 h\u00ecnh c\u00f3 b\u1ed1n \u0111\u1ec9nh c\u00e1ch \u0111\u1ec1u giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o n\u00ean lu\u00f4n n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n<br\/> C\u00e1c h\u00ecnh c\u00f2n l\u1ea1i kh\u00f4ng \u0111\u00fang <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":1535},{"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 h\u00ecnh v\u1ebd sau: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D6.png' \/><\/center> <br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y kh\u00f4ng \u0111\u00fang?","select":["A. B\u1ed1n \u0111i\u1ec3m $M,Q,N,C$ n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ","B. B\u1ed1n \u0111i\u1ec3m $A,N,M,B$ n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ","C. \u0110\u01b0\u1eddng tr\u00f2n \u0111i qua $A,\\,N,\\,B$ c\u00f3 t\u00e2m l\u00e0 trung \u0111i\u1ec3m \u0111o\u1ea1n $AB$","D. B\u1ed1n \u0111i\u1ec3m $A,B,M,C$ n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n"],"explain":" <span class='basic_left'> Ta c\u00f3: $AM\\bot BC;\\,BN\\bot AC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\left\\{ \\begin{align} & \\widehat{QNC}+\\widehat{QMC}={{90}^{o}}+{{90}^{o}}={{180}^{o}} \\\\ & \\widehat{BNA}+\\widehat{BMA}={{90}^{o}}+{{90}^{o}}={{180}^{o}} \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow $ T\u1ee9 gi\u00e1c $MQNC; ANMB$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> Hay b\u1ed1n \u0111i\u1ec3m $MQNC$ n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 b\u1ed1n \u0111i\u1ec3m $ANMB$ n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <br\/> Tam gi\u00e1c $ANB$ vu\u00f4ng t\u1ea1i $N$ n\u00ean t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c l\u00e0 trung \u0111i\u1ec3m \u0111o\u1ea1n $AB$ <br\/> Do ba \u0111i\u1ec3m $B,M,C$ th\u1eb3ng h\u00e0ng n\u00ean kh\u00f4ng t\u1ed3n t\u1ea1i \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111i\u1ec3m tr\u00ean <br\/> Suy ra kh\u1eb3ng \u0111\u1ecbnh A, B, C \u0111\u00fang, kh\u1eb3ng \u0111\u1ecbnh D sai.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span><\/span>","column":1}]}],"id_ques":1536},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Trong c\u00e1c kh\u1eb3ng \u0111\u1ecbnh sau, h\u00e3y ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh kh\u00f4ng \u0111\u00fang.<br\/> M\u1ed9t t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c n\u1ebfu: ","select":["A. T\u1ee9 gi\u00e1c c\u00f3 g\u00f3c ngo\u00e0i t\u1ea1i m\u1ed9t \u0111\u1ec9nh b\u1eb1ng g\u00f3c trong c\u1ee7a \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n ","B. T\u1ee9 gi\u00e1c c\u00f3 t\u1ed5ng hai g\u00f3c \u0111\u1ed1i di\u1ec7n b\u1eb1ng $180^o$ ","C. T\u1ee9 gi\u00e1c c\u00f3 t\u1ed5ng hai g\u00f3c b\u1eb1ng $180^o$","D. T\u1ee9 gi\u00e1c c\u00f3 hai \u0111\u1ec9nh c\u00f9ng nh\u00ecn c\u1ea1nh ch\u1ee9a hai \u0111\u1ec9nh c\u00f2n l\u1ea1i d\u01b0\u1edbi m\u1ed9t g\u00f3c $\\alpha $"],"explain":" <span class='basic_left'> D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp l\u00e0: <br\/> 1. T\u1ee9 gi\u00e1c c\u00f3 g\u00f3c ngo\u00e0i t\u1ea1i m\u1ed9t \u0111\u1ec9nh b\u1eb1ng g\u00f3c trong c\u1ee7a \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n <br\/> 2. T\u1ee9 gi\u00e1c c\u00f3 t\u1ed5ng hai g\u00f3c \u0111\u1ed1i di\u1ec7n b\u1eb1ng $180^o$ <br\/> 3. T\u1ee9 gi\u00e1c c\u00f3 hai \u0111\u1ec9nh c\u00f9ng nh\u00ecn c\u1ea1nh ch\u1ee9a hai \u0111\u1ec9nh c\u00f2n l\u1ea1i d\u01b0\u1edbi m\u1ed9t g\u00f3c <br\/> 4. T\u1ee9 gi\u00e1c c\u00f3 b\u1ed1n \u0111\u1ec9nh c\u00e1ch \u0111\u1ec1u m\u1ed9t \u0111i\u1ec3m <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh kh\u00f4ng \u0111\u00fang l\u00e0 C<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C <\/span><\/span>","column":1}]}],"id_ques":1537},{"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'> Trong c\u00e1c h\u00ecnh v\u1ebd t\u1ee9 gi\u00e1c $ABCD$ sau, h\u00e3y ch\u1ecdn h\u00ecnh kh\u00f4ng ph\u1ea3i l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n","select":["A. <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D8.1.png' \/> ","B. <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D8.2.png' \/> ","C. <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D8.3.png' \/>","D. <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D8.4.png' \/>"],"explain":" <span class='basic_left'> \u0110\u00e1p \u00e1n A v\u00e0 B c\u00f3 t\u1ed5ng hai g\u00f3c \u0111\u1ed1i nhau b\u1eb1ng $180^o$ n\u00ean n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n <br\/> \u0110\u00e1p \u00e1n C c\u00f3 g\u00f3c ngo\u00e0i t\u1ea1i m\u1ed9t \u0111\u1ec9nh b\u1eb1ng g\u00f3c trong c\u1ee7a \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n n\u00ean n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n <br\/> Suy ra h\u00ecnh D kh\u00f4ng ph\u1ea3i l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":1538},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho h\u00ecnh thoi $ABCD$, g\u1ecdi $O$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $AC$ v\u00e0 $BD$; $M, N, P, Q$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh $AB, BC, CD, DA$. Ch\u1ee9ng minh $MNPQ$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[3],[4],[1],[5],[2]]],"list":[{"point":5,"left":["T\u01b0\u01a1ng t\u1ef1: $OP=\\dfrac{1}{2}AD;\\,ON=\\dfrac{1}{2}AB;\\,OQ=\\dfrac{1}{2}CD$ ","M\u00e0 $AB=BC=CD=DA$ (\u0111\u1ecbnh ngh\u0129a h\u00ecnh thoi) <br\/> $\\Rightarrow OM=ON=OP=OQ$ ","V\u00ec $M$ l\u00e0 trung \u0111i\u1ec3m $AB, O$ l\u00e0 trung \u0111i\u1ec3m $AC$ n\u00ean $MO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$"," $\\Rightarrow MNPQ$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","$\\Rightarrow MO=\\dfrac{1}{2}BC$(t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh)"],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D9.png' \/><\/center> <br\/> V\u00ec $M$ l\u00e0 trung \u0111i\u1ec3m $AB, O$ l\u00e0 trung \u0111i\u1ec3m $AC$ n\u00ean $MO$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$ <br\/> $\\Rightarrow MO=\\dfrac{1}{2}BC$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh) <br\/> T\u01b0\u01a1ng t\u1ef1: $OP=\\dfrac{1}{2}AD;\\,ON=\\dfrac{1}{2}AB;\\,OQ=\\dfrac{1}{2}CD$ <br\/> M\u00e0 $AB=BC=CD=DA$ (\u0111\u1ecbnh ngh\u0129a h\u00ecnh thoi) <br\/> $\\Rightarrow OM=ON=OP=OQ$ <br\/> $\\Rightarrow MNPQ$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1539},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D10.png' \/><\/center> <br\/> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$ v\u00e0 $M$ l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m b\u00ean ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n. T\u1eeb $M$ v\u1ebd hai ti\u1ebfp tuy\u1ebfn $MA, MB$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n ($A, B$ l\u00e0 hai ti\u1ebfp \u0111i\u1ec3m). Qua $M$ v\u1ebd c\u00e1t tuy\u1ebfn $MCD$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n. G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $CD$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $AIOB$ n\u1ed9i ti\u1ebfp. ","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],[4],[1]]],"list":[{"point":5,"left":["$OI\\bot CD$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) $\\Rightarrow \\widehat{OIM}={{90}^{o}}$ ","$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ A,I,B$ c\u00f9ng nh\u00ecn $OM$ d\u01b0\u1edbi g\u00f3c $90^o$","$\\Rightarrow A,I,O,B,M$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) hay $AIOB$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n","Ta c\u00f3: $\\widehat{OAM}=\\widehat{OBM}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn)"],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D10.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{OAM}=\\widehat{OBM}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) <br\/> $OI\\bot CD$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow \\widehat{OIM}={{90}^{o}}$ <br\/> $\\Rightarrow A,I,B$ c\u00f9ng nh\u00ecn $OM$ d\u01b0\u1edbi g\u00f3c $90^o$ <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $A,I,O,B,M$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) hay $AIOB$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n <\/span>"}]}],"id_ques":1540},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$, c\u00e1c \u0111\u01b0\u1eddng cao $BD, CE$ c\u1ee7a tam gi\u00e1c $ABC$ c\u1eaft nhau t\u1ea1i $H$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $ADHE$ n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[1],[2],[3]]],"list":[{"point":5,"left":["$\\Rightarrow AEHD$ n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) "," Ta c\u00f3: $CE\\bot AB;\\,BD\\bot AC$ (gi\u1ea3 thi\u1ebft) ","$\\Rightarrow \\widehat{AEH}=\\widehat{ADH}={{90}^{o}}$","$\\Rightarrow $ C\u00e1c \u0111i\u1ec3m $E,D$ c\u00f9ng nh\u00ecn $AH$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D11.png' \/><\/center> <br\/> Ta c\u00f3: $CE\\bot AB;\\,BD\\bot AC$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow \\widehat{AEH}=\\widehat{ADH}={{90}^{o}}$ <br\/> $\\Rightarrow $ C\u00e1c \u0111i\u1ec3m $E,D$ c\u00f9ng nh\u00ecn $AH$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$ <br\/> $\\Rightarrow AEHD$ n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1541},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ v\u00e0 m\u1ed9t \u0111i\u1ec3m $D$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $B$. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BD,$ \u0111\u01b0\u1eddng th\u1eb3ng $CD $ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $F$. Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c $AFBC$ n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[3],[2],[4],[1]]],"list":[{"point":5,"left":["$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ F,A$ c\u00f9ng nh\u00ecn $BC$ d\u01b0\u1edbi g\u00f3c $90^o$ ","$\\widehat{BAC}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) ","$\\Rightarrow AFBC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","Ta c\u00f3: $\\widehat{BFD}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D12.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{BFD}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\widehat{BAC}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ F,A$ c\u00f9ng nh\u00ecn $BC$ d\u01b0\u1edbi g\u00f3c $90^o$ <br\/> $\\Rightarrow AFBC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1542},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$, d\u00e2y $AB$ v\u00e0 \u0111i\u1ec3m $C$ \u1edf ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n n\u1eb1m tr\u00ean tia $AB$. T\u1eeb \u0111i\u1ec3m ch\u00ednh gi\u1eefa $P$ c\u1ee7a cung l\u1edbn $AB$ k\u1ebb \u0111\u01b0\u1eddng k\u00ednh $PQ$ c\u1eaft d\u00e2y $AB$ t\u1ea1i $D$. Tia $CP$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $I$, $AB$ c\u1eaft $QI$ t\u1ea1i $K$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $PDKI$ n\u1ed9i ti\u00eap. ","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],[2],[4]]],"list":[{"point":5,"left":["$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ D,I$ c\u00f9ng nh\u00ecn $PK$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$ ","Ta c\u00f3: $PQ\\bot AB$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) $\\Rightarrow \\widehat{PDK}={{90}^{o}}$ ","$\\widehat{PIQ}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n)","$\\Rightarrow PDKI$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D13.png' \/><\/center> <br\/> Ta c\u00f3: $PQ\\bot AB$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow \\widehat{PDK}={{90}^{o}}$ <br\/> $\\widehat{PIQ}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ D,I$ c\u00f9ng nh\u00ecn $PK$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$ <br\/> $\\Rightarrow PDKI$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1543},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D14.png' \/><\/center> <br\/> Cho n\u0103m \u0111i\u1ec3m th\u1eb3ng h\u00e0ng theo th\u1ee9 t\u1ef1 l\u00e0 $A, B, C, D, E$ sao cho $AB = BC = CD = DE= R$. V\u1ebd c\u00e1c \u0111\u01b0\u1eddng tr\u00f2n $(C; 2R)$ v\u00e0 $(B; R)$. D\u00e2y $MN$ c\u1ee7a $(C)$ vu\u00f4ng g\u00f3c v\u1edbi $AD$ t\u1ea1i $D$. $AM$ c\u1eaft $(B)$ t\u1ea1i \u0111i\u1ec3m th\u1ee9 hai l\u00e0 $K$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $KMDC$ n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[1],[2],[3]]],"list":[{"point":5,"left":["$\\Rightarrow KMDC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) ","$\\widehat{AKC}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) $\\Rightarrow \\widehat{CKM}={{90}^{o}}$ ","Ta c\u00f3: $\\widehat{CDM}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft)","$\\Rightarrow $ C\u00e1c \u0111i\u1ec3m $K,D$ nh\u00ecn $MC$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D14.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{CDM}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\widehat{AKC}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow \\widehat{CKM}={{90}^{o}}$ <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ K,D$ nh\u00ecn $MC$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$ <br\/> $\\Rightarrow KMDC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1544},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111o\u1ea1n th\u1eb3ng $AB$ v\u00e0 m\u1ed9t \u0111i\u1ec3m $C$ n\u1eb1m gi\u1eefa $A$ v\u00e0 $B$. Tr\u00ean n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd $AB$ v\u1ebd hai tia $Ax, By$ c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi $AB$. Tr\u00ean tia $Ax$ l\u1ea5y m\u1ed9t \u0111i\u1ec3m $I$, tia vu\u00f4ng g\u00f3c v\u1edbi $CI$ t\u1ea1i $C$ c\u1eaft $By$ t\u1ea1i $K$. \u0110\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $IC$ c\u1eaft $IK$ t\u1ea1i $P$. Ch\u1ee9ng minh $CPKB$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp. ","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":["$\\widehat{CPI}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) $\\Rightarrow \\widehat{CPK}={{90}^{o}}$","$\\Rightarrow CPKB$ n\u1ed9i ti\u1ebfp trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) ","$\\Rightarrow \\widehat{CPK}+\\widehat{CBK}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$ ","Ta c\u00f3: $\\widehat{CBK}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft)"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D15.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{CBK}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\widehat{CPI}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> $\\Rightarrow \\widehat{CPK}={{90}^{o}}$ <br\/> $\\Rightarrow \\widehat{CPK}+\\widehat{CBK}={{90}^{o}}+{{90}^{o}}={{180}^{o}}$ <br\/> $\\Rightarrow CPKB$ n\u1ed9i ti\u1ebfp trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1545},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Tr\u00ean hai c\u1ea1nh c\u1ee7a m\u1ed9t g\u00f3c vu\u00f4ng $xOy$ l\u1ea5y hai \u0111i\u1ec3m $A$ v\u00e0 $B$ sao cho $OA = OB$. M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng qua $A$ c\u1eaft $OB$ t\u1ea1i $M$ ($M$ n\u1eb1m gi\u1eefa $O$ v\u00e0 $B$). T\u1eeb $B$ h\u1ea1 \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u1edbi $AM$ t\u1ea1i $H$. Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $AOHB$ n\u1ed9i ti\u1ebfp. ","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],[2]]],"list":[{"point":5,"left":["$\\Rightarrow AOHB$ n\u1ed9i ti\u1ebfp trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) ","Ta c\u00f3: $\\widehat{OAB}=\\widehat{AHB}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) ","$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ O,H$ c\u00f9ng nh\u00ecn $AB$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D16.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{OAB}=\\widehat{AHB}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ O,H$ c\u00f9ng nh\u00ecn $AB$ d\u01b0\u1edbi m\u1ed9t g\u00f3c $90^o$ <br\/> $\\Rightarrow AOHB$ n\u1ed9i ti\u1ebfp trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1546},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["12"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" <span class='basic_left'>Tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ c\u00f3 $AB = 8cm$, $AC=15cm$, \u0111\u01b0\u1eddng cao $AH=5cm$ (\u0111i\u1ec3m $H$ n\u1eb1m ngo\u00e0i c\u1ea1nh $BC$). T\u00ednh b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $R=$_input_ $(cm)$","hint":"K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $AD$ r\u1ed3i x\u00e9t c\u1eb7p tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D17.png' \/><\/center> <br\/> K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $AD$ c\u1ee7a $(O)$ <br\/> $\\Rightarrow \\widehat{ACD}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> Ta c\u00f3 $ABCD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow \\widehat{ABH}=\\widehat{ADC}$ (g\u00f3c ngo\u00e0i t\u1ea1i m\u1ed9t \u0111\u1ec9nh b\u1eb1ng g\u00f3c trong c\u1ee7a \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n) <br\/> X\u00e9t $\\Delta ABH$ v\u00e0 $\\Delta ADC$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & \\widehat{AHB}=\\widehat{ACD}={{90}^{o}} \\\\ & \\widehat{ABH}=\\widehat{ADC} \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta ABH\\sim \\Delta ADC$ (g.g) <br\/> $\\Rightarrow \\dfrac{AB}{AD}=\\dfrac{AH}{AC}$ (t\u1ec9 s\u1ed1 \u0111\u1ed3ng d\u1ea1ng) <br\/> $\\Rightarrow \\dfrac{8}{2R}=\\dfrac{5}{15}\\Rightarrow R=\\dfrac{8.15}{2.5}=12\\,\\left( cm \\right)$<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12$ <\/span><\/span> "}]}],"id_ques":1547},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho tam gi\u00e1c nh\u1ecdn $ABC$, \u0111\u01b0\u1eddng cao $AD$. G\u1ecdi $AM, AN$ l\u00e0 c\u00e1c ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $BC$ ($M, N$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). Ch\u1ee9ng minh $AMDN$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp.","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":["$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ M,D,N$ c\u00f9ng nh\u00ecn c\u1ea1nh $AO$ d\u01b0\u1edbi g\u00f3c $90^o$ ","$\\Rightarrow AMDN$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp "," Ta c\u00f3: $\\widehat{OMA}=\\widehat{ONA}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn)","$\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ A,M,D,O,N$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","$\\widehat{ODA}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft)"],"top":60,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D18.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{OMA}=\\widehat{ONA}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) <br\/> $\\widehat{ODA}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ M,D,N$ c\u00f9ng nh\u00ecn c\u1ea1nh $AO$ d\u01b0\u1edbi g\u00f3c $90^o$ <br\/> $\\Rightarrow$ C\u00e1c \u0111i\u1ec3m $ A,M,D,O,N$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow AMDN$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp <\/span>"}]}],"id_ques":1548},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho h\u00ecnh thang $ABCD$ c\u00f3 \u0111\u00e1y l\u1edbn $AD$, \u0111\u00e1y nh\u1ecf $BC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O)$. Ch\u1ee9ng minh $ABCD$ l\u00e0 h\u00ecnh thang c\u00e2n. ","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],[1],[4]]],"list":[{"point":5,"left":[" Do $AD\/\/BC$ $\\Rightarrow \\widehat{BCD}+\\widehat{CDA}={{180}^{o}}$ (t\u1ed5ng hai g\u00f3c trong c\u00f9ng ph\u00eda) (2) "," T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{CDA}=\\widehat{BAD}$ ","Ta c\u00f3 $ABCD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O)$ <br\/> $\\Rightarrow \\widehat{BCD}+\\widehat{BAD}={{180}^{o}}$ (t\u1ed5ng hai g\u00f3c \u0111\u1ed1i di\u1ec7n) (1)","$\\Rightarrow ABCD$ l\u00e0 h\u00ecnh thang c\u00e2n "],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D19.png' \/><\/center> <br\/>Ta c\u00f3 $ABCD$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O)$ <br\/> $\\Rightarrow \\widehat{BCD}+\\widehat{BAD}={{180}^{o}}$ (t\u1ed5ng hai g\u00f3c \u0111\u1ed1i di\u1ec7n) (1) <br\/> Do $AD\/\/BC$ $\\Rightarrow \\widehat{BCD}+\\widehat{CDA}={{180}^{o}}$ (t\u1ed5ng hai g\u00f3c trong c\u00f9ng ph\u00eda) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{CDA}=\\widehat{BAD}$ <br\/> $\\Rightarrow ABCD$ l\u00e0 h\u00ecnh thang c\u00e2n <\/span>"}]}],"id_ques":1549},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$. Tr\u00ean ti\u1ebfp tuy\u1ebfn t\u1ea1i $B$ c\u1ee7a n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n, l\u1ea5y c\u00e1c \u0111i\u1ec3m $C$ v\u00e0 $D\\, (BC < BD)$. C\u00e1c tia $AC$ v\u00e0 $AD$ c\u1eaft n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n theo th\u1ee9 t\u1ef1 t\u1ea1i $F$ v\u00e0 $E$ (kh\u00e1c $A$). Ch\u1ee9ng minh $CDEF$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp. ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[1],[5],[4],[3]]],"list":[{"point":5,"left":[" $\\Rightarrow \\widehat{ABE}=\\widehat{ADB}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{DAB}$) "," Ta c\u00f3: $\\widehat{AEB}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n); $\\widehat{ABD}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) ","$\\Rightarrow CDEF$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)"," $\\Rightarrow \\widehat{ADB}=\\widehat{AFE}$","M\u1eb7t kh\u00e1c $\\widehat{AFE}=\\widehat{ABE}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) "],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai17/lv1/img\/h935_D20.png' \/><\/center> <br\/>Ta c\u00f3: $\\widehat{AEB}={{90}^{o}}$ (g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n); <br\/> $\\widehat{ABD}={{90}^{o}}$ (t\u00ednh ch\u1ea5t ti\u1ebfp tuy\u1ebfn) <br\/> $\\Rightarrow \\widehat{ABE}=\\widehat{ADB}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{DAB}$) <br\/> M\u1eb7t kh\u00e1c $\\widehat{AFE}=\\widehat{ABE}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) <br\/> $\\Rightarrow \\widehat{ADB}=\\widehat{AFE}$ <br\/> $\\Rightarrow CDEF$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1550}],"lesson":{"save":0,"level":1}}