{"segment":[{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$, \u0111i\u1ec3m $M$ chuy\u1ec3n \u0111\u1ed9ng tr\u00ean c\u1ea1nh $AC$. K\u1ebb $CH$ vu\u00f4ng g\u00f3c v\u1edbi $BM$, Khi $M$ di chuy\u1ec3n tr\u00ean c\u1ea1nh $AC$ th\u00ec \u0111i\u1ec3m $H$ di chuy\u1ec3n tr\u00ean \u0111\u01b0\u1eddng n\u00e0o?","select":["A. \u0110\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$ ","B. \u0110\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $AC$ ","C. Cung nh\u1ecf $AC$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$","D. Cung nh\u1ecf $BC$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $AC$"],"explain":" <span class='basic_left'><center> <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K1.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{BHC}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> M\u00e0 $BC$ c\u1ed1 \u0111\u1ecbnh n\u00ean \u0111i\u1ec3m $H$ lu\u00f4n nh\u00ecn $BC$ d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng <br\/> $\\Rightarrow $ \u0110i\u1ec3m $H$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$ <br\/> Gi\u1edbi h\u1ea1n qu\u1ef9 t\u00edch: <br\/> Khi $M\\equiv A$ th\u00ec $H\\equiv A$. <br\/> Khi $M\\equiv C$ th\u00ec $H\\equiv C$ <br\/> V\u1eady $H$ thu\u1ed9c cung nh\u1ecf $AC$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh $BC$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C <\/span> <br\/> <b> Ch\u00fa \u00fd: <\/b> Khi \u0111i\u1ec3m $M$ b\u1ecb gi\u1edbi h\u1ea1n ($M$ di chuy\u1ec3n tr\u00ean c\u1ea1nh $AC$) th\u00ec qu\u1ef9 t\u00edch \u0111i\u1ec3m $H$ c\u0169ng b\u1ecb gi\u1edbi h\u1ea1n. Th\u00f4ng th\u01b0\u1eddng h\u1ecdc sinh hay m\u1eafc sai l\u1ea7m khi b\u1ecf qua b\u01b0\u1edbc n\u00e0y.<\/span>","column":2}]}],"id_ques":1641},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["60"],["75"],["45"]]],"list":[{"point":10,"width":50,"ques":"T\u00ednh c\u00e1c g\u00f3c c\u1ee7a tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O;R)$, bi\u1ebft r\u1eb1ng $AC=R\\sqrt{3};AB=R\\sqrt{2}$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{ABC} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o; \\widehat{BAC} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o; \\widehat{ACB} = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} ^o$","hint":"T\u00ednh c\u00e1c g\u00f3c \u1edf t\u00e2m $AOB;AOC$ r\u1ed3i suy ra s\u1ed1 \u0111o c\u00e1c g\u00f3c $ACB; ABC$ qua h\u1ec7 qu\u1ea3 c\u1ee7a g\u00f3c n\u1ed9i ti\u1ebfp","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K2.png' \/><\/center> <br\/> Ta c\u00f3: $O{{A}^{2}}+O{{B}^{2}}={{R}^{2}}+{{R}^{2}}=2{{R}^{2}}=A{{B}^{2}}$ <br\/> $\\Rightarrow \\Delta OAB$ vu\u00f4ng t\u1ea1i $O$ (\u0111\u1ecbnh l\u00ed Pitago \u0111\u1ea3o) <br\/> $\\Rightarrow \\widehat{AOB}={{90}^{o}}$ <br\/> $\\Rightarrow \\widehat{ACB}={{45}^{o}}$ (h\u1ec7 qu\u1ea3 g\u00f3c n\u1ed9i ti\u1ebfp) <br\/>G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$ <br\/> $\\Rightarrow \\left\\{ \\begin{align} & OH\\bot AC \\\\ & AH=HC=\\dfrac{R\\sqrt{3}}{2} \\\\ \\end{align} \\right.$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> X\u00e9t $\\Delta AHO$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $\\sin \\widehat{AOH}=\\dfrac{AH}{AO}=\\dfrac{\\dfrac{R\\sqrt{3}}{2}}{R}=\\dfrac{\\sqrt{3}}{2}$ <br\/> $\\Rightarrow \\widehat{AOH}={{60}^{o}}$ <br\/> X\u00e9t $\\Delta OAC$ c\u00f3: <br\/> $OA=OC=R$ <br\/> $\\Rightarrow \\Delta OAC$ c\u00e2n t\u1ea1i $O$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> M\u00e0 $OH$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c $\\Rightarrow \\widehat{AOC}=2\\widehat{AOH}={{2.60}^{o}}={{120}^{o}}$ <br\/> $\\Rightarrow \\widehat{ABC}={{60}^{o}}$ (h\u1ec7 qu\u1ea3 c\u1ee7a g\u00f3c n\u1ed9i ti\u1ebfp) <br\/> M\u1eb7t kh\u00e1c $\\widehat{ABC}+\\widehat{ACB}+\\widehat{BAC}={{180}^{o}}$ (t\u1ed5ng ba g\u00f3c c\u1ee7a tam gi\u00e1c $ABC$) <br\/> $\\begin{align} \\Rightarrow \\widehat{BAC} & ={{180}^{o}}-\\widehat{ABC}-\\widehat{ACB} \\\\ & ={{180}^{o}}-{{60}^{o}}-{{45}^{o}}={{75}^{o}} \\\\ \\end{align}$ <br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $60; 75$ v\u00e0 $45$ <\/span><\/span><\/span> "}]}],"id_ques":1642},{"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":10,"width":50,"type_input":"","ques":"<span class='basic_left'> Qua \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O)$, k\u1ebb c\u00e1c ti\u1ebfp tuy\u1ebfn $MA, MB$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n ($A,B$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi $C$ l\u00e0 m\u1ed9t \u0111i\u1ec3m b\u1ea5t k\u00ec thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n. $D, E, F$ theo th\u1ee9 t\u1ef1 l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $C$ tr\u00ean $AB, MA, MB$. <br\/> <b> C\u00e2u 1: <\/b> H\u00e3y so s\u00e1nh hai g\u00f3c $BDF$ v\u00e0 $AED$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{BDF}$ _input_ $\\widehat{AED}$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K3.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{DAC}=\\widehat{CBF}$ (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 $\\overset\\frown{BC}$) <br\/> $\\Rightarrow \\widehat{ACD}=\\widehat{BCF}$ (c\u00f9ng ph\u1ee5 v\u1edbi hai g\u00f3c b\u1eb1ng nhau) (1) <br\/> T\u1ee9 gi\u00e1c $ADEC$ c\u00f3 c\u00e1c \u0111i\u1ec3m $D, E$ c\u00f9ng nh\u00ecn $AC$ d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng <br\/> N\u00ean $ADEC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow \\widehat{AED}=\\widehat{ACD}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn $\\overset\\frown{AD}$) (2) <br\/> T\u1ee9 gi\u00e1c $BDCF$ c\u00f3 c\u00e1c \u0111i\u1ec3m $D, F$ c\u00f9ng nh\u00ecn $BC$ d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng <br\/> N\u00ean $BDCF$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1ee3c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow \\widehat{BDF}=\\widehat{BCF}$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn $\\overset\\frown{BF}$) (3) <br\/> T\u1eeb (1), (2), (3) $\\Rightarrow \\widehat{AED}=\\widehat{BDF}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$ <\/span><\/span> "}]}],"id_ques":1643},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Qua \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O)$, k\u1ebb c\u00e1c ti\u1ebfp tuy\u1ebfn $MA, MB$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n ($A,B$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi $C$ l\u00e0 m\u1ed9t \u0111i\u1ec3m b\u1ea5t k\u00ec thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n. $D, E, F$ theo th\u1ee9 t\u1ef1 l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $C$ tr\u00ean $AB, MA, MB$. <br\/> <b> C\u00e2u 2: <\/b> Ch\u1ee9ng minh r\u1eb1ng $AE.BF = AD.BD$","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":10,"left":["X\u00e9t $\\Delta DAE$ v\u00e0 $\\Delta FBD$ c\u00f3: $\\left\\{ \\begin{align} & \\widehat{DAE}=\\widehat{DBF}\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & \\widehat{AED}=\\widehat{BDF}\\,\\left( \\text{theo c\u00e2u 1} \\right) \\\\ \\end{align} \\right.$","$\\Rightarrow AE.BF=AD.BD$ "," Ta c\u00f3: $MA=MB$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\Delta MAB$ c\u00e2n t\u1ea1i $M$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) "," $\\Rightarrow \\Delta DAE\\sim \\Delta FBD\\,(g.g)$ <br\/> $\\Rightarrow \\dfrac{AD}{BF}=\\dfrac{AE}{BD}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7)"," $\\Rightarrow \\widehat{MAB}=\\widehat{MBA}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{DAE}=\\widehat{DBF}$ (c\u00f9ng b\u00f9 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/bai20/lv3/img\/h938_K3.png' \/><\/center> <br\/> Ta c\u00f3: $MA=MB$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\Delta MAB$ 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\/> $\\Rightarrow \\widehat{DAE}=\\widehat{DBF}$ (c\u00f9ng b\u00f9 v\u1edbi hai g\u00f3c b\u1eb1ng nhau) <br\/> X\u00e9t $\\Delta DAE$ v\u00e0 $\\Delta FBD$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & \\widehat{DAE}=\\widehat{DBF}\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & \\widehat{AED}=\\widehat{BDF}\\,\\left( \\text{theo c\u00e2u 1} \\right) \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta DAE\\sim \\Delta FBD\\,(g.g)$ <br\/> $\\Rightarrow \\dfrac{AD}{BF}=\\dfrac{AE}{BD}$ (c\u1eb7p c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7) <br\/> $\\Rightarrow AE.BF=AD.BD$ <\/span>"}]}],"id_ques":1644},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"N\u1ebfu hai \u0111\u01b0\u1eddng th\u1eb3ng $AB$ v\u00e0 $CD$ c\u1eaft nhau t\u1ea1i $M$ sao cho $MA.MB = MC.MD$ th\u00ec b\u1ed1n \u0111i\u1ec3m $A, B, C, D$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n","select":["A. \u0110\u00fang","B. Sai "],"hint":"X\u00e9t c\u1eb7p tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng v\u00e0 d\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t c\u1ee7a c\u1eb7p tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng \u0111\u1ec3 ch\u1ee9ng minh","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K5.png' \/><\/center> <br\/> X\u00e9t $\\Delta AMD$ v\u00e0 $\\Delta MCB$ c\u00f3: <br\/> $\\widehat{M}$ chung <br\/> $MA.MB=MC.MD \\Rightarrow \\dfrac{MA}{MC}=\\dfrac{MD}{MB}$ <br\/> $\\Rightarrow \\Delta MAD\\sim \\Delta MCB\\,\\left( c.g.c \\right)$ <br\/> $\\Rightarrow \\widehat{MAD}=\\widehat{MCB}$ (c\u1eb7p g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\Rightarrow$ T\u1ee9 gi\u00e1c $ABCD$ n\u1ed9i ti\u1ebfp m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <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> <br\/><b> Ch\u00fa \u00fd: <\/b> \u0110\u1ea3o l\u1ea1i, ta c\u0169ng ch\u1ee9ng minh \u0111\u01b0\u1ee3c: N\u1ebfu hai c\u00e1t tuy\u1ebfn $AB$ v\u00e0 $CD$ c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau t\u1ea1i $M$ th\u00ec $MA. MB = MC.MD$ <\/span>","column":2}]}],"id_ques":1645},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$ v\u00e0 \u0111i\u1ec3m $A$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3. K\u1ebb c\u00e1c ti\u1ebfp tuy\u1ebfn $AB, AC$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n $(O)$ ($B, C$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $OA$ v\u00e0 $BC$. K\u1ebb d\u00e2y cung $DE$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ qua $I$. <br\/> <b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh b\u1ed1n \u0111i\u1ec3m $A, D, O, E$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[2],[7],[6],[5],[3],[1]]],"list":[{"point":10,"left":[" $\\Rightarrow \\Delta IDC\\sim \\Delta IBE\\,\\left( g.g \\right)$ <br\/> $\\Rightarrow \\dfrac{ID}{IB}=\\dfrac{IC}{IE}\\Rightarrow ID.IE=IB.IC=I{{B}^{2}}$ (1)"," M\u00e0 $AI$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean l\u00e0 trung tuy\u1ebfn $\\Rightarrow IB=IC$ "," $\\Rightarrow $ B\u1ed1n \u0111i\u1ec3m $A, D, O, E$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (\u00e1p d\u1ee5ng k\u1ebft qu\u1ea3 c\u1ee7a b\u00e0i t\u1eadp tr\u00ean) ","$\\Rightarrow B{{I}^{2}}=AI.IO$ (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow IA.IO=IE.ID$","X\u00e9t $\\Delta ABO$ c\u00f3: <br\/> $\\widehat{ABO}={{90}^{o}}\\,\\left( \\text{t\u00ednh ch\u1ea5t trung tuy\u1ebfn} \\right)$; $BI\\bot AO$ "," X\u00e9t $\\Delta IDC$ v\u00e0 $\\Delta IBE$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & \\widehat{DIC}=\\widehat{BIE}\\,\\left( \\text{hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh} \\right) \\\\ & \\widehat{DEB}=\\widehat{DCB}\\,\\left( \\text{hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung} \\right) \\\\ \\end{align} \\right.$"," X\u00e9t $\\Delta ABC$ c\u00f3: $AB=AC$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\Delta ABC$ c\u00e2n t\u1ea1i $A$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n)"],"top":110,"hint":"S\u1eed d\u1ee5ng k\u1ebft qu\u1ea3 c\u1ee7a b\u00e0i t\u1eadp tr\u01b0\u1edbc ch\u1ee9ng minh $IA.IO = IE.ID$ suy ra t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K6.png' \/><\/center> <br\/> X\u00e9t $\\Delta ABC$ c\u00f3: <br\/> $AB=AC$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\Delta ABC$ c\u00e2n t\u1ea1i $A$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> M\u00e0 $AI$ l\u00e0 \u0111\u01b0\u1eddng cao n\u00ean l\u00e0 trung tuy\u1ebfn $\\Rightarrow IB=IC$ <br\/> X\u00e9t $\\Delta IDC$ v\u00e0 $\\Delta IBE$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & \\widehat{DIC}=\\widehat{BIE}\\,\\left( \\text{hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh} \\right) \\\\ & \\widehat{DEB}=\\widehat{DCB}\\,\\left( \\text{hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung} \\right) \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta IDC\\sim \\Delta IBE\\,\\left( g.g \\right)$ <br\/> $\\Rightarrow \\dfrac{ID}{IB}=\\dfrac{IC}{IE}\\Rightarrow ID.IE=IB.IC=I{{B}^{2}}$ (1) <br\/> X\u00e9t $\\Delta ABO$ c\u00f3: <br\/> $\\widehat{ABO}={{90}^{o}}\\,\\left( \\text{t\u00ednh ch\u1ea5t trung tuy\u1ebfn} \\right)$ <br\/> $BI\\bot AO$ <br\/> $\\Rightarrow B{{I}^{2}}=AI.IO$ (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow IA.IO=IE.ID$ <br\/> $\\Rightarrow $ B\u1ed1n \u0111i\u1ec3m $A, D, O, E$ c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (\u00e1p d\u1ee5ng k\u1ebft qu\u1ea3 c\u1ee7a b\u00e0i t\u1eadp tr\u00ean) <\/span>"}]}],"id_ques":1646},{"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":10,"width":50,"type_input":"","ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$ v\u00e0 \u0111i\u1ec3m $A$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3. K\u1ebb c\u00e1c ti\u1ebfp tuy\u1ebfn $AB, AC$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n $(O)$ ($B, C$ l\u00e0 c\u00e1c ti\u1ebfp \u0111i\u1ec3m). G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $OA$ v\u00e0 $BC$. K\u1ebb d\u00e2y cung $DE$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ qua $I$. <br\/> <b> C\u00e2u 2: <\/b> So s\u00e1nh hai g\u00f3c $\\widehat{BAD}$ v\u00e0 $\\widehat{CAE}$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{BAD}$ _input_ $\\widehat{CAE}$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K6.png' \/><\/center> <br\/> Theo c\u00e2u 1, ta c\u00f3 $ADOE$ l\u00e0 t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow\\left\\{ \\begin{align} & \\widehat{EAO}=\\widehat{EDO} \\\\ & \\widehat{DAO}=\\widehat{DEO} \\\\ \\end{align} \\right.$ (hai g\u00f3c n\u1ed9i ti\u1ebfp c\u00f9ng ch\u1eafn m\u1ed9t cung) (1) <br\/> X\u00e9t $\\Delta ODE$ c\u00f3: <br\/> $OD=OE$ (c\u00f9ng b\u1eb1ng b\u00e1n k\u00ednh c\u1ee7a $(O)$) <br\/> $\\Rightarrow \\Delta ODE$ c\u00e2n t\u1ea1i $O$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> $\\Rightarrow \\widehat{ODE}=\\widehat{OED}$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\widehat{EAO}=\\widehat{DAO}$ (3) <br\/> M\u00e0 $\\widehat{BAO}=\\widehat{CAO}$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow \\widehat{BAE}=\\widehat{CAD}$ (4) <br\/> T\u1eeb (3) v\u00e0 (4) $\\Rightarrow \\widehat{CAD}+\\widehat{DAE}=\\widehat{BAE}+\\widehat{DAE}$ <br\/> $\\Rightarrow \\widehat{CAE}=\\widehat{BAD}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$ <\/span><\/span> "}]}],"id_ques":1647},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["6"]]],"list":[{"point":10,"width":50,"ques":"Cho hai \u0111\u01b0\u1eddng tr\u00f2n \u0111\u1ed3ng t\u00e2m t\u1ea1o th\u00e0nh m\u1ed9t h\u00ecnh v\u00e0nh kh\u0103n. Bi\u1ebft r\u1eb1ng \u0111\u01b0\u1eddng tr\u00f2n nh\u1ecf c\u00f3 b\u00e1n k\u00ednh l\u00e0 $4cm$ v\u00e0 h\u00ecnh v\u00e0nh kh\u0103n c\u00f3 di\u1ec7n t\u00edch $20\\pi \\,c{{m}^{2}}.$ B\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn l\u00e0 _input_ $(cm)$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K8.png' \/><\/center> <br\/> G\u1ecdi ${{S}_{1}}$ l\u00e0 di\u1ec7n t\u00edch \u0111\u01b0\u1eddng tr\u00f2n nh\u1ecf, ${{S}_{2}}$ l\u00e0 di\u1ec7n t\u00edch \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn, $S$ l\u00e0 di\u1ec7n t\u00edch v\u00e0nh kh\u0103n <br\/> Di\u1ec7n t\u00edch \u0111\u01b0\u1eddng tr\u00f2n nh\u1ecf l\u00e0: ${{S}_{1}}=\\pi {{.4}^{2}}=16\\pi \\,\\left( c{{m}^{2}} \\right)$ <br\/> M\u00e0 di\u1ec7n t\u00edch h\u00ecnh v\u00e0nh kh\u0103n b\u1eb1ng: $S={{S}_{2}}-{{S}_{1}}$ <br\/> $\\Rightarrow {{S}_{2}}={{S}_{1}}+S=20\\pi +16\\pi =36\\pi \\,\\left( c{{m}^{2}} \\right)$ <br\/> B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn l\u00e0: $R=\\sqrt{\\dfrac{{{S}_{2}}}{\\pi }}=\\sqrt{\\dfrac{36\\pi }{\\pi }}=6\\,\\left( cm \\right)$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6$ <\/span><\/span><\/span> "}]}],"id_ques":1648},{"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 $\\Delta ABC$ c\u00f3 $BC$ c\u1ed1 \u0111\u1ecbnh, \u0111i\u1ec3m $A$ thu\u1ed9c n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd $BC$ sao cho $\\widehat{BAC}=\\alpha $. Qu\u1ef9 t\u00edch tr\u1ecdng t\u00e2m $G$ c\u1ee7a tam gi\u00e1c $ABC$ l\u00e0:","select":["A. M\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n","B. M\u1ed9t cung tr\u00f2n","C. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $BC$","D. \u0110\u01b0\u1eddng ph\u00e2n ph\u00e1c c\u1ee7a g\u00f3c $A$"],"explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K9.png' \/><\/center><br\/> G\u1ecdi $O$ l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp $\\Delta ABC$, $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BC$ <br\/> Ta c\u00f3: $\\widehat{BAC}=\\alpha $ n\u00ean \u0111i\u1ec3m $A$ thu\u1ed9c cung ch\u1ee9a g\u00f3c $\\alpha $ d\u1ef1ng tr\u00ean \u0111o\u1ea1n $BC$ (cung $BC$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$) <br\/> Do $\\alpha $ kh\u00f4ng \u0111\u1ed5i n\u00ean $O$ c\u1ed1 \u0111\u1ecbnh v\u00e0 $AO$ kh\u00f4ng \u0111\u1ed5i <br\/> Do $BC$ c\u1ed1 \u0111\u1ecbnh n\u00ean $M$ c\u1ed1 \u0111\u1ecbnh <br\/> L\u1ea5y $E$ thu\u1ed9c $MO$ sao cho $\\dfrac{ME}{MO}=\\dfrac{1}{3}$ $\\Rightarrow E$ c\u1ed1 \u0111\u1ecbnh <br\/> Ta c\u00f3: $\\dfrac{MG}{MA}=\\dfrac{1}{3}$ (t\u00ednh ch\u1ea5t tr\u1ecdng t\u00e2m tam gi\u00e1c) <br\/> $\\Rightarrow \\dfrac{MA}{MG}=\\dfrac{ME}{MO}$ <br\/> $\\Rightarrow EG\/\/AO$ (\u0111\u1ecbnh l\u00ed Ta-let \u0111\u1ea3o) <br\/> $\\Rightarrow \\dfrac{EG}{AO}=\\dfrac{1}{3}$ (h\u1ec7 qu\u1ea3 \u0111\u1ecbnh l\u00ed Ta-let) <br\/> $\\Rightarrow EG=\\dfrac{1}{3}AO$ <br\/> Do $AO$ kh\u00f4ng \u0111\u1ed5i n\u00ean $EG$ kh\u00f4ng \u0111\u1ed5i <br\/> Suy ra $G$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $E$ b\u00e1n k\u00ednh $\\dfrac{AO}{3}$ <br\/> Gi\u1edbi h\u1ea1n qu\u1ef9 t\u00edch: <br\/> Khi $A\\equiv B$ th\u00ec $G\\equiv I$, khi $A\\equiv C$ th\u00ec $G\\equiv H$ <br\/> Suy ra qu\u1ef9 t\u00edch c\u00e1c \u0111i\u1ec3m $G$ n\u1eb1m tr\u00ean cung $IH$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $E$ thu\u1ed9c n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd $BC$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B <\/span><\/span>","column":2}]}],"id_ques":1649},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["8"]]],"list":[{"point":10,"width":50,"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$, cung nh\u1ecf $AB$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 s\u1ed1 \u0111o ${{120}^{o}}.$ Ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ v\u00e0 $B$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau t\u1ea1i $D$. v\u1ebd \u0111\u01b0\u1eddng tr\u00f2n $(P)$ ti\u1ebfp x\u00fac v\u1edbi $AD, BD$ v\u00e0 cung $AB$. T\u00ednh chu vi \u0111\u01b0\u1eddng tr\u00f2n $(P)$, bi\u1ebft b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n $(O)$ l\u00e0 $12cm$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> Chu vi c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(P)$ l\u00e0 _input_ $\\pi (cm)$","hint":"G\u1ecdi $I$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $OD$ v\u00e0 $(O)$, k\u1ebb ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $I$ c\u1eaft $DA$ t\u1ea1i $E$, c\u1eaft $DB$ t\u1ea1i $F$. Ch\u1ee9ng minh tam gi\u00e1c $DEF$ \u0111\u1ec1u v\u00e0 $(P)$ l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp $\\Delta DEF$ n\u00ean t\u00ednh \u0111\u01b0\u1ee3c b\u00e1n k\u00ednh c\u1ee7a $(P)$. T\u1eeb \u0111\u00f3 t\u00ednh \u0111\u01b0\u1ee3c chu vi c\u1ee7a $(P)$ ","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai20/lv3/img\/h938_K10.png' \/><\/center> <br\/> Ta c\u00f3: $\\widehat{AOB}=\\text{s\u0111}\\widehat{AB}={{120}^{o}}$ (\u0111\u1ecbnh l\u00ed g\u00f3c \u1edf t\u00e2m) <br\/> $\\widehat{OAD}=\\widehat{OBD}={{90}^{o}}$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> $\\Rightarrow $ C\u00e1c \u0111i\u1ec3m $A, B$ c\u00f9ng nh\u00ecn $OD$ d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng <br\/> $\\Rightarrow $ T\u1ee9 gi\u00e1c $OADB$ n\u1ed9i ti\u1ebfp trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <br\/> $\\Rightarrow \\widehat{AOB}+\\widehat{ADB}={{180}^{o}}$ (t\u00ednh ch\u1ea5t t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp) <br\/> $\\Rightarrow \\widehat{ADB}={{180}^{o}}-\\widehat{AOB}={{180}^{o}}-{{120}^{o}}={{60}^{o}}$ (1) <br\/> $\\Rightarrow \\widehat{ADO}=\\dfrac{1}{2}\\widehat{ADB}=\\dfrac{1}{2}{{.60}^{o}}={{30}^{o}}$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) <br\/> X\u00e9t $\\Delta OAD$ vu\u00f4ng t\u1ea1i $A$ c\u00f3: <br\/> $OD=\\dfrac{OA}{\\sin \\widehat{ADO}}=\\dfrac{12}{\\dfrac{1}{2}}=24\\,\\left( cm \\right)$ <br\/> G\u1ecdi $I=OD\\cap \\left( O \\right)$, ti\u1ebfp tuy\u1ebfn t\u1ea1i $I$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft $AD$ t\u1ea1i $E$, c\u1eaft $BD$ t\u1ea1i $F$ <br\/> $\\Rightarrow DE=DF$ (t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow \\Delta DEF$ \u0111\u1ec1u (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow P$ l\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c $DEF$ <br\/> $\\Rightarrow PI=\\dfrac{1}{3}DI=\\dfrac{1}{3}\\left( OD-OI \\right)=\\dfrac{1}{3}\\left( 24-12 \\right)=4\\,\\left( cm \\right)$ <br\/> Chu vi \u0111\u01b0\u1eddng tr\u00f2n $(P)$ l\u00e0 $C=2\\pi .4=8\\pi \\,\\left( cm \\right)$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $8$ <\/span><\/span><\/span> "}]}],"id_ques":1650}],"lesson":{"save":0,"level":3}}