{"segment":[{"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'> Trong h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 $Oxy$, cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $I(1; 1)$, b\u00e1n k\u00ednh 4. H\u00e3y x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111i\u1ec3m $M(3; 0)$ \u0111\u1ed1i v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n. <\/span> ","select":["A. $M$ n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n ","B. $M$ n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n","C. $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n"],"hint":"Bi\u1ec3u di\u1ec5n h\u00ecnh tr\u00ean h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_21.png' \/><\/center> D\u1ec5 th\u1ea5y $M$ n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span>","column":1}],"id_ques":1271},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["9"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho hai \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$; $(O'; r)$ v\u00e0 \u0111o\u1ea1n n\u1ed1i t\u00e2m $d$. H\u00e3y \u0111i\u1ec1n gi\u00e1 tr\u1ecb th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng trong b\u1ea3ng sau <table><tr><th>$R (cm)$<br><\/th><th> $r (cm)$<br><\/th><th>$d (cm)$<br><\/th> <th>V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a $(O)$ v\u00e0 $(O')$<br><\/th> <\/tr><tr><td>_input_<\/td><td>3<\/td><td>4<\/td> <td>Ti\u1ebfp x\u00fac trong <\/td> <\/tr><tr><td>6<\/td><td>3<\/td><td>_input_<\/td> <td>Ti\u1ebfp x\u00fac ngo\u00e0i<\/td> <\/tr><\/table>","explain":"<span class='basic_left'> Hai \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac trong n\u1ebfu v\u00e0 ch\u1ec9 n\u1ebfu <br\/> $ d = R - r$ <br\/> $\\Rightarrow R = d + r$$ = 3 + 4 $$= 7\\, (cm)$ <br\/> Hai \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac ngo\u00e0i n\u1ebfu v\u00e0 ch\u1ec9 n\u1ebfu <br\/> $ d = R + r$ $= 6 + 3 $$= 9\\, (cm)$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $7$ v\u00e0 $9.$ <\/span> <\/span>"}],"id_ques":1272},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"C\u00f3 bao nhi\u00eau \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t? ","select":["A. M\u1ed9t ","B. Hai","C. V\u00f4 s\u1ed1","D. Kh\u00f4ng c\u00f3"],"explain":" <span class='basic_left'> \u0110\u01b0\u1eddng tr\u00f2n t\u00e2m $I$ \u0111i qua hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t $A$ v\u00e0 $B$ th\u00ec $IA = IB$ <br\/> Suy ra $I$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c $d$ c\u1ee7a $AB$ <br\/> M\u00e0 c\u00f3 v\u00f4 s\u1ed1 \u0111i\u1ec3m thu\u1ed9c $d$ <br\/> V\u1eady c\u00f3 v\u00f4 s\u1ed1 \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><\/span>","column":4}],"id_ques":1273},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"C\u00f3 bao nhi\u00eau \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111i\u1ec3m th\u1eb3ng h\u00e0ng? ","select":["A. M\u1ed9t ","B. Hai","C. V\u00f4 s\u1ed1","D. Kh\u00f4ng c\u00f3"],"explain":" Kh\u00f4ng t\u1ed3n t\u1ea1i \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111i\u1ec3m th\u1eb3ng h\u00e0ng <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D. <\/span>","column":4}],"id_ques":1274},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_22.png' \/><\/center> <br\/> Bi\u1ebft $OK$ b\u1eb1ng $1 cm$, $OH$ b\u1eb1ng $3 cm$, $CD$ b\u1eb1ng $6 cm$. T\u00ednh \u0111\u1ed9 d\u00e0i d\u00e2y $AB$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $AB =$ _input_ $(cm)$ <\/span>","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_22.1.png' \/><\/center> Ta c\u00f3: $OH\\bot AB$$\\Rightarrow H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $OK\\bot CD$$\\Rightarrow K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $CD$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow CK=\\dfrac{CD}{2}$$=3(cm)$ <br\/> $\\Delta OKC$ vu\u00f4ng t\u1ea1i $K$ <br\/> $OC^2 = OK^2 + CK^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OC=\\sqrt{O{{K}^{2}}+C{{K}^{2}}}$ <br\/> $=\\sqrt{3^2 + 1^2}$ <br\/> $=\\sqrt{10}(cm)$ <br\/> $\\Rightarrow OA=OC$$=\\sqrt{10} (cm)$ <br\/> $\\Delta AHO$ vu\u00f4ng t\u1ea1i $H$ <br\/> $OA^2 = OH^2 + AH^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow AH=\\sqrt{A{{O}^{2}}-O{{H}^{2}}}$ <br\/> $=1\\,(cm)$ <br\/> $\\Rightarrow AB=2AH$$=2\\,(cm)$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2.$ <\/span><\/span>"}],"id_ques":1275},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"\u0110\u1ec1 chung cho b\u1ed1n c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; 2 cm)$, \u0111\u01b0\u1eddng k\u00ednh AB. Tr\u00ean ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $AC = 3 cm$. $BC$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$. <br\/> <b> C\u00e2u a: <\/b> Khi \u0111\u00f3 \u0111\u1ed9 d\u00e0i $AD$ l\u00e0: ","select":["A. $1,2 cm$ ","B. $2,4 cm$","C. $2, 75 cm$","D. $ 4,8 cm$"],"hint":"S\u1eed d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_23.png' \/><\/center> Ta c\u00f3: $AB=2OA=4\\,(cm)$ <br\/> $AC$ l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a $(O)$ $\\Rightarrow \\widehat{CAB}={{90}^{o}}$ <br\/> X\u00e9t $\\Delta ABD$ c\u00f3: <br\/> $OA = OB = OD = 2cm$ <br\/> $\\Rightarrow \\Delta ADB$ vu\u00f4ng t\u1ea1i D (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow\\widehat{ADB}={{90}^{o}}$ <br\/> $\\Rightarrow AD\\bot BC$ <br\/>X\u00e9t $\\Delta ACB$ vu\u00f4ng t\u1ea1i $A$ $;AD\\bot BC$ <br\/> $\\dfrac{1}{A{{D}^{2}}}=\\dfrac{1}{A{{C}^{2}}}+\\dfrac{1}{A{{B}^{2}}}$ (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng)<br\/> $=\\dfrac{1}{9}+\\dfrac{1}{16}$ <br\/> $=\\dfrac{25}{144}$ <br\/> $\\Rightarrow A{{D}^{2}}=\\dfrac{144}{25}$ <br\/> $\\Rightarrow AD=\\dfrac{12}{5}$$=2,4(cm)$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B. <\/span><\/span>","column":4}],"id_ques":1276},{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; 2 cm)$, \u0111\u01b0\u1eddng k\u00ednh AB. Tr\u00ean ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $AC = 3 cm$. $BC$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$. G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD$, $K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$. <br\/> <b> C\u00e2u b: <\/b> Ch\u1ee9ng minh r\u1eb1ng b\u1ed1n \u0111i\u1ec3m $A, C, I, O$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n.<\/span>","title_trans":"S\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 c\u00e1c b\u01b0\u1edbc ch\u1ee9ng minh","temp":"sequence","correct":[[[4],[1],[3],[5],[6],[2]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_23.1.png","left":["X\u00e9t $\\Delta OAC$ vu\u00f4ng t\u1ea1i $A$ $\\Rightarrow HO=HC=HA$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn) (2) ","G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OC$ $\\Rightarrow HO= HC$"," X\u00e9t $\\Delta OIC$ vu\u00f4ng t\u1ea1i $I$ $\\Rightarrow HO=HC=HI$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn) (1) "," T\u1eeb (1) v\u00e0 (2) $\\Rightarrow HO=HC=HI=HA$ ","$\\Leftrightarrow A,C,I,O$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n","$I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD$ $\\Rightarrow OI\\bot BD$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow OI\\bot BC$ $\\Rightarrow \\widehat{OIC}={{90}^{o}}$"],"top":75,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_23.1.png' \/><\/center> G\u1ecdi $H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $OC$ $\\Rightarrow HO= HC$ <br\/> $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD$ <br\/> $\\Rightarrow OI\\bot BD$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow OI\\bot BC$ <br\/> $\\Rightarrow \\widehat{OIC}={{90}^{o}}$ <br\/> X\u00e9t $\\Delta OIC$ vu\u00f4ng t\u1ea1i $I$ <br\/> $\\Rightarrow HO=HC=HI$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (1) <br\/> X\u00e9t $\\Delta OAC$ vu\u00f4ng t\u1ea1i $A$ <br\/> $\\Rightarrow HO=HC=HA$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow HO=HC=HI=HA$ <br\/> $\\Leftrightarrow A,C,I,O$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <\/span>"}],"id_ques":1277},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho b\u1ed1n c\u00e2u","temp":"fill_the_blank","correct":[[["90"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; 2 cm)$, \u0111\u01b0\u1eddng k\u00ednh $AB.$ Tr\u00ean ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $AC = 3 cm$. $BC$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$. G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD$, $K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$. <br\/> <b> C\u00e2u c: <\/b> T\u00ednh s\u1ed1 \u0111o g\u00f3c $\\widehat{KDO}$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{KDO} =$ _input_ $^o$ <\/span>","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_23.2.png' \/><\/center>X\u00e9t $\\Delta ADC$ vu\u00f4ng t\u1ea1i $D$ <br\/> $K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$ <br\/> $\\Rightarrow KD=KA=KC$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> X\u00e9t $\\Delta KDO$ v\u00e0 $\\Delta KAO$ c\u00f3 <br\/> $KD=KA$ <br\/> $OA=OD$ <br\/> $OK$ chung <br\/> $\\Rightarrow \\Delta KDO=\\Delta KAO$ (c. c. c)<br\/> $\\Rightarrow \\widehat{KAO}=\\widehat{KDO}$$={{90}^{o}}$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $90.$ <\/span><\/span>"}],"id_ques":1278},{"title":"\u0110i\u1ec1n d\u1ea5u (>;<;=) th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; 2 cm)$, \u0111\u01b0\u1eddng k\u00ednh $AB.$ Tr\u00ean ti\u1ebfp tuy\u1ebfn t\u1ea1i $A$ l\u1ea5y \u0111i\u1ec3m $C$ sao cho $AC = 3 cm$. $BC$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i $D$. G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $BD$, $K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AC$. <br\/> <b> C\u00e2u d: <\/b> So s\u00e1nh hai g\u00f3c $ACO$ v\u00e0 $DCO$. <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\widehat{ACO} $ _input_ $\\widehat{DCO}$<\/span>","hint":"So s\u00e1nh $\\sin \\widehat{DCO}$ v\u00e0 $\\sin \\widehat{ACO}$ ","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai12/lv3/img\/h927_23.2.png' \/><\/center>X\u00e9t $\\Delta CAO$ vu\u00f4ng t\u1ea1i $A$ <br\/> $\\sin \\widehat{ACO}=\\dfrac{AO}{CO}$ <br\/> $\\Delta ICO$ vu\u00f4ng t\u1ea1i $I$ <br\/> $\\sin \\widehat{DCO}$$=\\sin \\widehat{ICO}=$$\\dfrac{IO}{CO}$ <br\/> M\u00e0 $IO < AO$ <br\/> $\\Rightarrow \\sin \\widehat{DCO}<\\sin \\widehat{ACO}$ <br\/> $\\Rightarrow \\widehat{DCO}<\\widehat{ACO}$ ( V\u00ec $\\widehat{DCO}$ v\u00e0 $\\widehat{ACO}$ nh\u1ecdn) <br\/><span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u $>$ <\/span><\/span>"}],"id_ques":1279},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"\u0110\u1ec1 chung cho b\u1ed1n c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"T\u00ednh b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh l\u00e0 $3cm, 4cm, 5cm$. ","select":["A. $0,5\\, cm$ ","B. $1\\, cm$","C. $2,5\\, cm$","D. $ 5\\, cm$"],"hint":"S\u1eed d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng","explain":" <span class='basic_left'> Ta c\u00f3: $3^2 + 4^2 $$= 5^2$ <br\/> $\\Rightarrow$ Tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c vu\u00f4ng (\u0111\u1ecbnh l\u00ed Pitago \u0111\u1ea3o) <br\/> Suy ra b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh huy\u1ec1n <br\/> V\u1eady b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp b\u1eb1ng $2,5\\, cm$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C. <\/span><\/span>","column":4}],"id_ques":1280}],"id_ques":0}],"lesson":{"save":1,"level":3,"time":44}}