Bài tập cơ bản bài Đường tròn, đường kính và dây cung

Home Lớp 9 Toán lớp 9 Đường tròn, đường kính và dây cung Bài tập cơ bản

{"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":"T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $MNP$ vu\u00f4ng t\u1ea1i $M$ l\u00e0:","select":["A. Trung \u0111i\u1ec3m c\u1ea1nh $PN$","B. Trung \u0111i\u1ec3m c\u1ea1nh $MP$","C. Trung \u0111i\u1ec3m c\u1ea1nh $MN$","D. Tr\u1ecdng t\u00e2m tam gi\u00e1c $MNP$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_1.jpg' \/><\/center> <br\/> G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $NP$. <br\/> Do $\\Delta MNP$ vu\u00f4ng t\u1ea1i $M$ <br\/> N\u00ean $MI = IN = IP$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow I $ l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp $\\Delta MNP$<br\/>$\\Rightarrow$ T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $MNP$ vu\u00f4ng t\u1ea1i $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ea1nh $PN$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span> <br\/> L\u01b0u \u00fd: <\/b> T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c vu\u00f4ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n.<\/span>","column":2}]}],"id_ques":1091},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn c\u1ee5m t\u1eeb th\u00edch h\u1ee3p \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua . . . c\u1ee7a m\u1ed9t d\u00e2y kh\u00f4ng \u0111i qua t\u00e2m th\u00ec . . . v\u1edbi d\u00e2y \u1ea5y.","select":["A. Trung \u0111i\u1ec3m, c\u1eaft","B. Giao \u0111i\u1ec3m, vu\u00f4ng g\u00f3c","C. Giao \u0111i\u1ec3m, c\u1eaft","D. Trung \u0111i\u1ec3m, vu\u00f4ng g\u00f3c"],"explain":" Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua trung \u0111i\u1ec3m <\/b> c\u1ee7a m\u1ed9t d\u00e2y kh\u00f4ng \u0111i qua t\u00e2m th\u00ec vu\u00f4ng g\u00f3c <\/b> v\u1edbi d\u00e2y \u1ea5y.<br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":2}]}],"id_ques":1092},{"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":[[["234"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"T\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $\\widehat{B}=90^o$, $AB =15 cm,$ $BC= 20 cm,$$ CD= 24 cm$ v\u00e0 $DA = 7 cm.$ <br\/> C\u00e2u 1: <\/b> Di\u1ec7n t\u00edch t\u1ee9 gi\u00e1c $ABCD =$ _input_ $(cm^2)$","explain":"H\u01b0\u1edbng d\u1eabn:<\/span><br\/> T\u00ednh c\u1ea1nh $AC$ v\u00e0 ch\u1ee9ng t\u1ecf cho tam gi\u00e1c $ADC$ vu\u00f4ng t\u1ea1i $D$. Di\u1ec7n t\u00edch t\u1ee9 gi\u00e1c $ABCD$ b\u1eb1ng t\u1ed5ng di\u1ec7n t\u00edch tam gi\u00e1c $ABC$ v\u00e0 $ADC$ B\u00e0i gi\u1ea3i:<br\/><\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D22a.jpg' \/><\/center><br\/> X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $B$ c\u00f3 <br\/> $AC^2=AB^2+BC^2 $ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow AC^2=15^2+20^2\\\\ \\Rightarrow AC^2=625 \\\\ \\Rightarrow AC= 25\\,(cm) $ <br\/> M\u00e0 $7^2+24^2=25^2$$\\Rightarrow AD^2+DC^2=AC^2$ <br\/> Suy ra $\\Delta ADC $ vu\u00f4ng t\u1ea1i $D$ (\u0111\u1ecbnh l\u00ed \u0111\u1ea3o Pitago) <br\/> $S_{ABCD}=S_{ABC}+S_{ADC}$ <br\/> $=\\dfrac{1}{2}AB.BC+\\dfrac{1}{2}AD.DC$ <br\/> $=\\dfrac{15.20}{2}+\\dfrac{7.24}{2}=234 $ (cm$^2$) <br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $234.$ <\/span><\/span>"}]}],"id_ques":1093},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u1ee9 gi\u00e1c $ABCD$ c\u00f3 $\\widehat{B}=90^o$, $AB =15 cm,$ $BC= 20 cm,$$ CD= 24 cm$ v\u00e0 $DA = 7 cm.$ <br\/> C\u00e2u 2: <\/b> Khi \u0111\u00f3 b\u1ed1n \u0111i\u1ec3m $A, B, C, D$ thu\u1ed9c c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ","select":["A. \u0110\u00fang","B. Sai"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D23.jpg' \/><\/center><br\/> G\u1ecdi O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC $\\Rightarrow OA = OC =\\dfrac{AC}{2}$ (1) <br\/> X\u00e9t $\\Delta ABC$ c\u00f3: <br\/> $ \\widehat{B}=90^o, OA=OC$ <br\/> $\\Rightarrow OB =\\dfrac{AC}{2}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (2)<br\/> X\u00e9t $\\Delta ADC$ c\u00f3: <br\/> $ \\widehat{D}=90^o, OA=OC$ <br\/> $\\Rightarrow OD =\\dfrac{AC}{2}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (3) <br\/> T\u1eeb (1), (2), (3) $\\Rightarrow OA=OB=OC=OD$ <br\/>Do \u0111\u00f3 4 \u0111i\u1ec3m A, B, C, D thu\u1ed9c c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n<br\/>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00fang<br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1094},{"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 h\u00ecnh vu\u00f4ng $MNPQ$ c\u00f3 c\u1ea1nh b\u1eb1ng $4 cm.$ Khi \u0111\u00f3 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp h\u00ecnh vu\u00f4ng \u0111\u00f3 b\u1eb1ng","select":["A. $2 \\,\\,cm$","B. $2\\sqrt{2}\\,cm$","C. $2\\sqrt{3}\\,cm$","D. $4\\sqrt{2}\\,cm$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D19.jpg' \/><\/center> <br\/> K\u1ebb $MP \\cap NQ = O$ <br\/> $\\Rightarrow OM = ON = OP=OQ$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh vu\u00f4ng) <br\/> $\\Rightarrow$ \u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp h\u00ecnh vu\u00f4ng $MNPQ$ c\u00f3 t\u00e2m $O,$ b\u00e1n k\u00ednh $OM$ <br\/> X\u00e9t $\\Delta MNP$ vu\u00f4ng t\u1ea1i $N$ c\u00f3: <br\/> $MP^2 = MN^2 + NP^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow MP=\\sqrt{MN^2 + NP^2}=\\sqrt{4^2+4^2}=4\\sqrt{2}\\,(cm)$ <br\/> $\\Rightarrow OM = \\dfrac{1}{2}MP=\\dfrac{1}{2}.4\\sqrt{2}=2\\sqrt{2} \\,(cm)$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":4}]}],"id_ques":1095},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"\u0110i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ khi v\u00e0 ch\u1ec9 khi ","select":["A. $OM = R$","B. $OM < R$","C. $OM > R$","D. $OM \\le R$"],"explain":" \u0110i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ khi v\u00e0 ch\u1ec9 khi $OM > R$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":4}]}],"id_ques":1096},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","f"]],"list":[{"ques":"Cho tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A,$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O.$ Trung tuy\u1ebfn $AM$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n \u1edf $D$","point":5,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D9a.jpg","col_name":["Kh\u1eb3ng \u0111\u1ecbnh","\u0110\u00fang","Sai"],"arr_ques":[" $AD$ l\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$<\/span> "," $\\widehat{ACD}=90^o$<\/span>"," $\\widehat{ABC}\\ne \\widehat{ADC}$<\/span>"],"explain":[" \u0110\u00fang, v\u00ec tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$ n\u00ean trung tuy\u1ebfn $AM$ \u0111\u1ed3ng th\u1eddi l\u00e0 trung tr\u1ef1c c\u1ee7a $BC.$ V\u00ec v\u1eady t\u00e2m $O$ n\u1eb1m tr\u00ean $AM,$ t\u1ee9c l\u00e0 $AD$ l\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a ($O$) <\/span>"," \u0110\u00fang, v\u00ec $\\Delta ACD$ c\u00f3: <br\/> $OA = OD\\Rightarrow OC$ l\u00e0 trung truy\u1ebfn c\u1ee7a $\\Delta ACD$ <br\/> M\u00e0 $OA= OC= OD = R$ <br\/> $\\Rightarrow OC = \\dfrac{1}{2}AD$ <br\/> $\\Rightarrow\\Delta ACD$ vu\u00f4ng t\u1ea1i $C$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{ACD}=90^o$ <\/span>"," Sai, ta c\u00f3: $\\left\\{ \\begin{align} & \\widehat{ABC}=\\widehat{ACB} \\\\ & AM \\bot BC \\\\ \\end{align} \\right.$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> M\u00e0 $\\widehat{ACB}=\\widehat{ADC}$ (c\u00f9ng ph\u1ee5 v\u1edbi $\\widehat{MCD}$) <br\/> Suy ra $\\widehat{ABC}=\\widehat{ADC}$ <\/span> "]}]}],"id_ques":1097},{"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":[[["8"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho $EF$ l\u00e0 d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; 5 cm).$ K\u1ebb $OH \\bot EF$ t\u1ea1i $H,$ bi\u1ebft $OH = 3 cm.$ <br\/> \u0110\u1ed9 d\u00e0i $EF=$_input_ (cm)","hint":"Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t d\u00e2y th\u00ec \u0111i qua trung \u0111i\u1ec3m c\u1ee7a d\u00e2y \u1ea5y","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_11.jpg' \/><\/center><br\/> Ta c\u00f3 $OH \\bot EF\\,$ <br\/> $\\Rightarrow EH=HF=\\dfrac{EF}{2}$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y)<br\/>$\\Delta HOE$ vu\u00f4ng t\u1ea1i $H$ <br\/> $OH^2+EH^2=OE^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow EH =\\sqrt{OE^2 - OH^2} $ <br\/> $ \\Rightarrow EH=\\sqrt{5^2-3^2}\\\\ \\Rightarrow EH = 4 \\,cm$ <br\/> Suy ra $EF =4.2= 8 \\,\\,(cm)$ <br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $8.$<\/span>"}]}],"id_ques":1098},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"N\u1ebfu $MN$ l\u00e0 m\u1ed9t d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; 3)$ th\u00ec","select":["A. $MN < 3$","B. $MN > 3$","C. $MN \\le 3$","D. $MN \\le 6$"],"explain":"$MN$ l\u00e0 d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; 3)$ <br\/> Do \u0111\u00f3 $MN \\le 2.3$$\\Leftrightarrow MN \\le 6$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":4}]}],"id_ques":1099},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $ABC$ b\u1ea5t k\u00ec l\u00e0:","select":["A. Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c $ABC$","B. Tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c $ABC$","C. Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c $ABC$","D. Giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c $ABC$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_2.jpg' \/><\/center> <br\/> K\u1ebb \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ v\u00e0 $AC$ c\u1eaft nhau t\u1ea1i $I$ <br\/> Do $I$ thu\u1ed9c trung tr\u1ef1c c\u1ee7a $AB$ <br\/> $\\Rightarrow IA = IB$ (t\u00ednh ch\u1ea5t trung tr\u1ef1c) <br\/> Do $I$ thu\u1ed9c trung tr\u1ef1c c\u1ee7a $AC$ <br\/> $\\Rightarrow IA = IC$ (t\u00ednh ch\u1ea5t trung tr\u1ef1c) <br\/> $\\Rightarrow IA = IA = IC $ <br\/> $\\Rightarrow I $ l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $ABC$ <br\/> Suy ra t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $ABC$ b\u1ea5t k\u00ec l\u00e0 giao \u0111i\u1ec3m ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c $ABC$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":1}]}],"id_ques":1100},{"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":[[["25"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $AC= 14 cm$ v\u00e0 $AB= 48 cm.$ <br\/> B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $ABC$ l\u00e0 _input_ $(cm)$","hint":"T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c vu\u00f4ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n","explain":" X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $ A$ <br\/> $BC^2=AB^2+AC^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $=14^2+48^2=2500$ <br\/> $\\Rightarrow BC=50\\,(cm)$ <br\/> Do t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c vu\u00f4ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n <br\/> $\\Rightarrow R=\\dfrac{BC}{2}=25\\,(cm)$<br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $25.$<\/span>"}]}],"id_ques":1101},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Bi\u1ec3n c\u1ea5m v\u01b0\u1ee3t l\u00e0 h\u00ecnh c\u00f3 t\u00e2m \u0111\u1ed1i x\u1ee9ng v\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D5.jpg' \/><\/center>","select":["A. \u0110\u00fang","B. Sai"],"explain":" $-$ H\u00ecnh n\u00e0y \u0111\u1ed1i x\u1ee9ng v\u1edbi h\u00ecnh kia qua \u0111i\u1ec3m O n\u1ebfu m\u1ed7i \u0111i\u1ec3m c\u1ee7a h\u00ecnh n\u00e0y \u0111\u1ed1i x\u1ee9ng v\u1edbi m\u1ed9t \u0111i\u1ec3m c\u1ee7a h\u00ecnh kia qua O, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.\u0110i\u1ec3m O g\u1ecdi l\u00e0 t\u00e2m \u0111\u1ed1i x\u1ee9ng c\u1ee7a hai h\u00ecnh \u0111\u00f3. <br\/> $-$ Hai h\u00ecnh g\u1ecdi l\u00e0 \u0111\u1ed1i x\u1ee9ng v\u1edbi nhau qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng n\u1ebfu m\u1ed7i \u0111i\u1ec3m c\u1ee7a h\u00ecnh n\u00e0y \u0111\u1ed1i x\u1ee9ng v\u1edbi m\u1ed9t \u0111i\u1ec3m thu\u1ed9c h\u00ecnh kia, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i. \u0110\u00e2y c\u0169ng g\u1ecdi l\u00e0 \u0111\u1ed1i x\u1ee9ng tr\u1ee5c. <br\/> Nh\u1eadn th\u1ea5y, bi\u1ec3n c\u1ea5m v\u01b0\u1ee3t l\u00e0 h\u00ecnh c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng v\u00e0 kh\u00f4ng c\u00f3 t\u00e2m \u0111\u1ed1i x\u1ee9ng <br\/> $\\Rightarrow$ Kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":1102},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn c\u1ee5m t\u1eeb th\u00edch h\u1ee3p \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 $Oxy,$ \u0111i\u1ec3m $B (-\\sqrt{7};\\sqrt{2}).$. . . \u0111\u01b0\u1eddng tr\u00f2n $(O; 3)$","select":["A. n\u1eb1m ngo\u00e0i","B. n\u1eb1m tr\u00ean","C. n\u1eb1m trong"],"hint":"T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n $OB$ r\u1ed3i so s\u00e1nh v\u1edbi $R$","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D4.png' \/><\/center><br\/> Ta c\u00f3: $OB=\\sqrt{(-\\sqrt{7})^2+(\\sqrt{2})^2}=3$ <br\/> $\\Rightarrow OB = R = 3$ <br\/> Suy ra \u0111i\u1ec3m $B$ n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; 3)$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":3}]}],"id_ques":1103},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u > , < , = th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho h\u00ecnh v\u1ebd: <br\/> <center> <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D2.png' \/> <\/center> <br\/> H\u00e3y so s\u00e1nh $EF$ v\u00e0 $GH$ <br\/> \u0110\u00e1p s\u1ed1: <\/b> $EF$ _input_ $GH$ ","hint":"Trong c\u00e1c d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y l\u1edbn nh\u1ea5t l\u00e0 \u0111\u01b0\u1eddng k\u00ednh","explain":" Ta c\u00f3 $EF$ l\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ <br\/> $GH$ kh\u00f4ng l\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ <br\/> V\u00ec trong c\u00e1c d\u00e2y c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y l\u1edbn nh\u1ea5t l\u00e0 \u0111\u01b0\u1eddng k\u00ednh <br\/> $\\Rightarrow EF > GH$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u $>$ <\/span>"}]}],"id_ques":1104},{"time":24,"part":[{"time":3,"title":"H\u00e3y n\u1ed1i m\u1ed7i \u00f4 \u1edf c\u1ed9t tr\u00e1i v\u1edbi m\u1ed9t \u00f4 \u1edf c\u1ed9t ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang: ","title_trans":"","audio":"","temp":"matching","correct":[["2","3","1"]],"list":[{"point":5,"image":"","left":["H\u00ecnh tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm$ g\u1ed3m t\u1eadp h\u1ee3p nh\u1eefng \u0111i\u1ec3m","\u0110\u01b0\u1eddng tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm$ g\u1ed3m t\u1eadp h\u1ee3p nh\u1eefng \u0111i\u1ec3m","T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn \u0111i\u1ec3m $I$ c\u1ed1 \u0111\u1ecbnh l\u00e0 $5 cm$"],"right":["l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm$","c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn $I$ nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng $5 cm$","c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn $I$ b\u1eb1ng $5 cm$"],"top":100,"explain":"H\u00ecnh tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm$ g\u1ed3m t\u1eadp h\u1ee3p nh\u1eefng \u0111i\u1ec3m c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn $I$ nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng $5 cm.$ <br\/>\u0110\u01b0\u1eddng tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm$ g\u1ed3m t\u1eadp h\u1ee3p nh\u1eefng \u0111i\u1ec3m c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn $I$ b\u1eb1ng $5 cm.$ <br\/>T\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00f3 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn \u0111i\u1ec3m $I$ c\u1ed1 \u0111\u1ecbnh l\u00e0 $5 cm$ l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $I$ b\u00e1n k\u00ednh $5 cm.$ "}]}],"id_ques":1105},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 h\u00ecnh c\u00f3:","select":["A. M\u1ed9t tr\u1ee5c \u0111\u1ed1i x\u1ee9ng","B. Hai tr\u1ee5c \u0111\u1ed1i x\u1ee9ng","C. V\u00f4 s\u1ed1 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng","D. Kh\u00f4ng c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng"],"explain":" \u0110\u01b0\u1eddng tr\u00f2n l\u00e0 h\u00ecnh c\u00f3 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. B\u1ea5t k\u00ec \u0111\u01b0\u1eddng k\u00ednh n\u00e0o c\u0169ng l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n <br\/>$\\Rightarrow$ \u0110\u01b0\u1eddng tr\u00f2n l\u00e0 h\u00ecnh c\u00f3 v\u00f4 s\u1ed1 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng.<br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":1106},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","f"]],"list":[{"point":5,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["Qua ba \u0111i\u1ec3m kh\u00f4ng th\u1eb3ng h\u00e0ng, ta v\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t v\u00e0 ch\u1ec9 m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. ","T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c vu\u00f4ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng.","Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t d\u00e2y th\u00ec vu\u00f4ng g\u00f3c v\u1edbi d\u00e2y \u1ea5y."],"hint":"","explain":["\u0110\u00fang, theo c\u00e1ch x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng tr\u00f2n","Sai, v\u00ec t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c vu\u00f4ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n. <br\/>","Sai, v\u00ec trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t d\u00e2y kh\u00f4ng \u0111i qua t\u00e2m th\u00ec vu\u00f4ng g\u00f3c v\u1edbi d\u00e2y \u1ea5y."]}]}],"id_ques":1107},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"\u0110i\u1ec3m $M$ thu\u1ed9c h\u00ecnh tr\u00f2n $(O; R)$ khi v\u00e0 ch\u1ec9 khi ","select":["A. $OM= R$","B. $OM < R$","C. $OM > R$","D. $OM \\le R$"],"explain":" \u0110i\u1ec3m $M$ thu\u1ed9c h\u00ecnh tr\u00f2n $(O; R)$ khi v\u00e0 ch\u1ec9 khi $OM \\le R$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":4}]}],"id_ques":1108},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ d\u00e2y $MN$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ v\u00e0 $\\widehat{MON}=60^o$. T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $MN$ theo $R.$ ","select":["A. $\\dfrac{R}{2}$","B. $\\dfrac{R\\sqrt{2}}{2}$","C. $\\dfrac{R\\sqrt{3}}{2}$","D. $\\dfrac{R}{6}$ "],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D14.jpg' \/><\/center> <br\/> K\u1ebb $OH\\bot MN$ t\u1ea1i $H$ <br\/> Ta c\u00f3: $OM = ON = R$ <br\/> $\\Rightarrow \\Delta OMN$ c\u00e2n (\u0111\u1ecbnh ngh\u0129a) <br\/> $\\Rightarrow \\widehat{MOH}=\\dfrac{\\widehat{ MON}}{2}=30^o$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao trong tam gi\u00e1c c\u00e2n) <br\/> X\u00e9t $\\Delta OHM$ vu\u00f4ng t\u1ea1i $ H$ <br\/> $ \\Rightarrow OH =OM.\\cos \\widehat{MOH}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $ \\Rightarrow OH = R.\\cos 30^o\\\\ \\Rightarrow OH=\\dfrac{\\sqrt{3}}{2}R$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":4}]}],"id_ques":1109},{"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 tam gi\u00e1c \u0111\u1ec1u $MNP$ c\u00f3 c\u1ea1nh b\u1eb1ng $5 cm.$ Khi \u0111\u00f3 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c \u0111\u00f3 b\u1eb1ng","select":["A. $5\\sqrt{3}\\,cm$ ","B. $2\\sqrt{3}\\,cm$ ","C. $\\dfrac{5\\sqrt{3}}{2}\\,cm$","D. $\\dfrac{5\\sqrt{3}}{3}\\,cm$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv1/img\/H921_D7.jpg' \/><\/center><br\/>H\u1ea1 $MH \\bot NP\\,$ <br\/> $\\Rightarrow NH = HP=\\dfrac{NP}{2}=2,5\\, cm$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao trong tam gi\u00e1c \u0111\u1ec1u)<br\/> Do $\\Delta MNP$ \u0111\u1ec1u n\u00ean t\u00e2m $O$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tr\u00f9ng v\u1edbi tr\u1ecdng t\u00e2m tam gi\u00e1c <br\/> Khi \u0111\u00f3 $R = MO=\\dfrac{2}{3}MH$ (t\u00ednh ch\u1ea5t tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c) <br\/> X\u00e9t $\\Delta MHN $ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $ MN^2 = MH^2 + NH^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow MH^2 = MN^2 - NH^2$ <br\/> $\\Rightarrow MH=\\sqrt{MN^2-NH^2}$$=\\sqrt{5^2-\\left(\\dfrac{5}{2}\\right)^2}=\\dfrac {5\\sqrt{3}}{2}\\, (cm)$ <br\/> $\\Rightarrow MO= \\dfrac{2}{3}.\\dfrac{5\\sqrt{3}}{2}$$=\\dfrac{5\\sqrt{3}}{3}\\,cm$ <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span><br\/>L\u01b0u \u00fd: <\/span> B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c \u0111\u1ec1u b\u1eb1ng hai ph\u1ea7n ba \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/span>","column":2}]}],"id_ques":1110}],"lesson":{"save":0,"level":1}}

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Câu hỏi này theo dạng chọn đáp án đúng, sau khi đọc xong câu hỏi, bạn bấm vào một trong số các đáp án mà chương trình đưa ra bên dưới, sau đó bấm vào nút gửi để kiểm tra đáp án và sẵn sàng chuyển sang câu hỏi kế tiếp

Trả lời đúng trong khoảng thời gian quy định bạn sẽ được + số điểm như sau:
Trong khoảng 1 phút đầu tiên	+ 5 điểm
Trong khoảng 1 phút -> 2 phút	+ 4 điểm
Trong khoảng 2 phút -> 3 phút	+ 3 điểm
Trong khoảng 3 phút -> 4 phút	+ 2 điểm
Trong khoảng 4 phút -> 5 phút	+ 1 điểm

Quá 5 phút: không được cộng điểm

Tổng thời gian làm mỗi câu (không giới hạn)

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