{"segment":[{"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":[[["120"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho $AB$ l\u00e0 m\u1ed9t d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; R).$ Bi\u1ebft $AB = R\\sqrt{3}$. <br\/> S\u1ed1 \u0111o g\u00f3c $\\widehat{AOB}$ l\u00e0_input_$^o$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K14.jpg' \/><\/center><br\/> V\u1ebd $OH \\bot AB$ t\u1ea1i $H.$ <br\/> Ta c\u00f3: $OA=OB = R$ <br\/> $\\Rightarrow \\Delta AOB$ c\u00e2n t\u1ea1i $O$ (\u0111\u1ecbnh ngh\u0129a tam gi\u00e1c c\u00e2n) <br\/> Suy ra $\\left\\{ \\begin{align} & HA=HB=\\dfrac{R\\sqrt{3}}{2} \\\\ & \\widehat{O_{1}}=\\widehat{O_{2}} \\\\ \\end{align} \\right.$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng cao trong tam gi\u00e1c c\u00e2n) <br\/> X\u00e9t $\\Delta AOH$ vu\u00f4ng t\u1ea1i $H$ <br\/> \u00c1p d\u1ee5ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn ta c\u00f3: <br\/> $\\sin \\widehat{O_{1}}=\\dfrac{AH}{OA}=\\dfrac{\\sqrt{3}}{2}$$\\Rightarrow \\widehat{O_{1}}=60^o$<br\/>Do \u0111\u00f3 $\\widehat{AOB}=2\\widehat{O_{1}}= 120^o$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $120.$<\/span><\/span>"}]}],"id_ques":1111},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<span class='basic_left'>Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ v\u00e0 ba d\u00e2y $AB, AC, AD.$ G\u1ecdi $M$ v\u00e0 $N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $B$ tr\u00ean c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $AC$ v\u00e0 $AD.$ Khi \u0111\u00f3 $MN \\le 2R.$<\/span>","select":["A. \u0110\u00fang","B. Sai"],"explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K12a.jpg' \/><\/center><br\/> G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ <br\/> X\u00e9t $\\Delta ANB $ c\u00f3: <br\/> $\\widehat{N}=90^o,$ $AI = IB $ <br\/> $\\Rightarrow AI=IB=IN$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (1) <br\/> X\u00e9t $\\Delta AMB $ c\u00f3: <br\/> $\\widehat{M}=90^o,$ $AI = IB $ <br\/> $\\Rightarrow AI=IB=IM$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) (2) <br\/> T\u1eeb (1), (2) suy ra $AI = IB = IN = IM$ <br\/> $\\Rightarrow$ B\u1ed1n \u0111i\u1ec3m $A, B, M, N$ thu\u1ed9c c\u00f9ng \u0111\u01b0\u1eddng tr\u00f2n $\\left( I; \\dfrac{AB}{2}\\right)$ <br\/> $\\Rightarrow MN \\le AB$ <br\/>X\u00e9t $(O; R)$ c\u00f3 $AB$ l\u00e0 d\u00e2y cung n\u00ean $AB \\le 2 R$ <br\/> Suy ra $MN \\le 2R$ <br\/> Do \u0111\u00f3 kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0111\u00fang <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":2}]}],"id_ques":1112},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R).$ V\u1ebd hai d\u00e2y $AB$ v\u00e0 $CD$ vu\u00f4ng g\u00f3c v\u1edbi nhau. Ch\u1ee9ng minh r\u1eb1ng $S_{ADBC}\\le 2R^2.$","title_trans":"S\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 c\u00e1c b\u01b0\u1edbc ch\u1ee9ng minh b\u00e0i to\u00e1n ","temp":"sequence","correct":[[[2],[1],[4],[3]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K11.jpg","left":["N\u00ean $AB \\le 2R$; $CD \\le 2R$","V\u00ec $AB, CD$ l\u00e0 c\u00e1c d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ ","$\\Rightarrow S_{ADBC}\\le 2R^2$ ","Do $AB \\bot CD$ $\\Rightarrow S_{ADBC}=\\dfrac{AB.CD}{2} \\le \\dfrac{2R.2R}{2}$"],"top":80,"explain":"<span class='basic_left'>V\u00ec $AB, CD$ l\u00e0 c\u00e1c d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ <br\/> N\u00ean $AB \\le 2R;$$ CD \\le 2R$ <br\/> Do $AB \\bot CD$ $\\Rightarrow S_{ADBC}=\\dfrac{AB.CD}{2} \\le \\dfrac{2R.2R}{2}$ <br\/> $\\Rightarrow S_{ADBC}\\le 2R^2$<\/span>"}]}],"id_ques":1113},{"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":[[["4"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Tam gi\u00e1c $ABC$ c\u00f3 c\u1ea1nh $BC$ c\u1ed1 \u0111\u1ecbnh, \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn $BM $ l\u00e0 $2 cm.$ \u0110\u1ec9nh $A$ di \u0111\u1ed9ng tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u1ed1 \u0111\u1ecbnh. Khi \u0111\u00f3, b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 _input_$(cm).$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K10.jpg' \/><\/center><br\/>Tr\u00ean tia \u0111\u1ed1i c\u1ee7a tia $BC$ l\u1ea5y \u0111i\u1ec3m $O$ sao cho $BO = BC$ <br\/> Do $BC$ c\u1ed1 \u0111\u1ecbnh $\\Rightarrow O$ l\u00e0 m\u1ed9t \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh <br\/> X\u00e9t $\\Delta OAC$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & AM=MC \\\\ & OB=BC \\\\ \\end{align} \\right.$ (gi\u1ea3 thi\u1ebft) <br\/>$\\Rightarrow BM$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta OAC$ <br\/> $\\Rightarrow BM =\\dfrac{OA}{2}$$\\Rightarrow OA = 2BM = 2.2 = 4 \\,(cm)$ <br\/>V\u1eady \u0111i\u1ec3m $A$ di \u0111\u1ed9ng tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; 4 cm)$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4.$<\/span><\/span>"}]}],"id_ques":1114},{"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":[[2]],"list":[{"point":10,"ques":"<span class='basic_left'> Cho h\u00ecnh thoi $ABCD,$ hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i $O.$ G\u1ecdi $H, I, K, L$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $O$ tr\u00ean c\u1ea1nh $AB, BC, CD, DA.$ <br\/><b> C\u00e2u 1: <\/b> Khi \u0111\u00f3 b\u1ed1n \u0111i\u1ec3m $H, I, K ,L$ kh\u00f4ng c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n<\/span>","select":["A. \u0110\u00fang","B. Sai"],"hint":"D\u00f9ng t\u00ednh ch\u1ea5t \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K7.jpg' \/><\/center><br\/>Ta c\u00f3: $ABCD$ l\u00e0 h\u00ecnh thoi (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow AO$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{BAD}$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thoi) <br\/> Suy ra $OH = OL$ (t\u00ednh ch\u1ea5t \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c th\u00ec c\u00e1ch \u0111\u1ec1u hai c\u1ea1nh c\u1ee7a g\u00f3c) <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u00f3: $OH = OI; OI =OK$ <br\/> $\\Rightarrow OH = OI = OK =OL$<br\/> $\\Rightarrow$ B\u1ed1n \u0111i\u1ec3m $H, I, K, L$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n $(O; OH)$ <br\/> V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":1115},{"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":[[["1"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho h\u00ecnh thoi $ABCD,$ hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i $O.$ G\u1ecdi $H, I, K, L$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a $O$ tr\u00ean c\u1ea1nh $AB, BC, CD, DA.$ <br\/><b> C\u00e2u 2: <\/b> T\u00ednh b\u00e1n k\u00ednh $R$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua b\u1ed1n \u0111i\u1ec3m $H, I, K, L$ bi\u1ebft $\\widehat{BAD}=60^o;$$\\, AC= 4 cm.$<br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $R = $ _input_ $(cm).$<\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K7.jpg' \/><\/center><br\/><span class='basic_left'> Ta c\u00f3 $AO = OC =\\dfrac{AC}{2}=2\\,(cm)$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thoi) <br\/> $\\widehat{BAO}=\\dfrac{\\widehat{BAD}}{2}=30^o$ (t\u00ednh ch\u1ea5t h\u00ecnh thoi) <br\/> X\u00e9t $\\Delta AOH$ vu\u00f4ng t\u1ea1i $ H$: <br\/> \u00c1p d\u1ee5ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn ta c\u00f3: <br\/> $OH=OA.\\sin \\widehat{BAC}$$=2.\\sin 30^o=1\\,(cm)$ <br\/> <span class='basic_pink'> V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $1.$ <\/span><\/span>"}]}],"id_ques":1116},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A.$ Tr\u00ean c\u1ea1nh $AB, AC$ l\u1ea7n l\u01b0\u1ee3t l\u1ea5y c\u00e1c \u0111i\u1ec3m $D$ v\u00e0 $E.$ G\u1ecdi $M, N, P ,Q$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $DE, EB, BC, CD.$ Khi \u0111\u00f3, b\u1ed1n \u0111i\u1ec3m $M, N, P , Q$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n.","select":["A. \u0110\u00fang","B. Sai"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $MNPQ$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh <br\/><b> B\u01b0\u1edbc 2:<\/b> Ch\u1ee9ng minh $\\widehat{NMQ}=90^o$ <br\/><b> B\u01b0\u1edbc 3:<\/b> Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $MNPQ$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K6.jpg' \/><\/center><br\/>K\u1ebb $MP \\cap NQ = O$ <br\/> D\u1ec5 th\u1ea5y $MN$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh trong $\\Delta EDB$ <br\/> $\\Rightarrow MN \/\/ DB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh) <br\/> D\u1ec5 th\u1ea5y $PQ$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh trong $\\Delta CDB$ <br\/> $\\Rightarrow PQ \/\/ DB$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh) <br\/> $\\Rightarrow MN \/\/ PQ$ (c\u00f9ng song song v\u1edbi $DB$) <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1: $MQ \/\/ NP$ (c\u00f9ng song song v\u1edbi $EC$) <br\/> Suy ra t\u1ee9 gi\u00e1c $MNPQ$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (\u0111\u1ecbnh ngh\u0129a) <br\/> Do $MN\/\/ BD\\Rightarrow MN \/\/ AB $ <br\/> M\u00e0 $ AB \\bot AC \\Rightarrow MN \\bot AC$ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta \u0111\u01b0\u1ee3c: $MQ \\bot MN$$\\Rightarrow \\widehat{NMQ} = 90^o$.<br\/> $\\Rightarrow$ T\u1ee9 gi\u00e1c $MNPQ$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow OM =ON = OP = OQ$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o h\u00ecnh ch\u1eef nh\u1eadt) <br\/> Suy ra b\u1ed1n \u0111i\u1ec3m $M, N, P , Q$ c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n <br\/> V\u1eady 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\/><span class='basic_green'>L\u01b0u \u00fd: <\/span> B\u1ed1n \u0111\u1ec9nh c\u1ee7a m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt bao gi\u1edd c\u0169ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o, c\u00f3 b\u00e1n k\u00ednh b\u1eb1ng n\u1eeda m\u1ed7i \u0111\u01b0\u1eddng ch\u00e9o.<\/span>","column":2}]}],"id_ques":1117},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ G\u1ecdi $M$ l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m gi\u1eefa $A$ v\u00e0 $B.$ Qua $M$ v\u1ebd d\u00e2y $CD$ vu\u00f4ng g\u00f3c v\u1edbi $AB.$ L\u1ea5y \u0111i\u1ec3m $E$ \u0111\u1ed1i x\u1ee9ng v\u1edbi $A$ qua $M$ <br\/><b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh t\u1ee9 gi\u00e1c $ACED$ l\u00e0 h\u00ecnh thoi.","title_trans":"S\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 c\u00e1c b\u01b0\u1edbc ch\u1ee9ng minh b\u00e0i to\u00e1n ","temp":"sequence","correct":[[[3],[4],[1],[2]]],"list":[{"point":10,"image":"https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K5.jpg","left":[" $ME = MA$ (gi\u1ea3 thi\u1ebft) <br\/> Suy ra $ACED$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","M\u00e0 $AE\\bot CD$ t\u1ea1i $M$ <br\/> $\\Rightarrow ACED$ l\u00e0 h\u00ecnh thoi (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)","X\u00e9t t\u1ee9 gi\u00e1c $ACED,$ ta c\u00f3:","$AB \\bot CD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow MC = MD$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y)"],"top":100,"explain":"<span class='basic_left'> X\u00e9t t\u1ee9 gi\u00e1c $ACED,$ ta c\u00f3: <br\/> $AB \\bot CD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow MC = MD$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> $ME = MA$ (gi\u1ea3 thi\u1ebft) <br\/> Suy ra $ACED$ l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> M\u00e0 $AE\\bot CD$ t\u1ea1i $M$ <br\/> $\\Rightarrow ACED$ l\u00e0 h\u00ecnh thoi (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <\/span>"}]}],"id_ques":1118},{"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":[[["12"]]],"list":[{"point":10,"width":60,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R),$ \u0111\u01b0\u1eddng k\u00ednh $AB.$ G\u1ecdi $M$ l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m gi\u1eefa $A$ v\u00e0 $B.$ Qua $M$ v\u1ebd d\u00e2y $CD$ vu\u00f4ng g\u00f3c v\u1edbi $AB.$ L\u1ea5y \u0111i\u1ec3m $E$ \u0111\u1ed1i x\u1ee9ng v\u1edbi $A$ qua $M$ <br\/><b> C\u00e2u 2: <\/b> Bi\u1ebft $R =6,5 cm$ v\u00e0 $MA = 4 cm.$ Khi \u0111\u00f3, \u0111\u1ed9 d\u00e0i $CD $ l\u00e0_input_ $(cm).$ <\/span>","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> Ch\u1ee9ng minh $\\Delta ACB$ vu\u00f4ng t\u1ea1i $C$ <br\/><b> B\u01b0\u1edbc 2: <\/b> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng \u0111\u1ec3 t\u00ednh c\u1ea1nh $MC.$ T\u1eeb \u0111\u00f3 suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh $CD$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<br\/><\/span><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K5.jpg' \/><\/center><br\/>$\\Delta ABC$ c\u00f3: <br\/> $ OC =\\dfrac{AB}{2} = R$ <br\/> $\\Rightarrow \\Delta ABC$ vu\u00f4ng t\u1ea1i $C$ (\u0111\u1ecbnh l\u00ed trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/>Ta c\u00f3 $AB =2R = 13 \\,(cm) $$\\Rightarrow MB= AB - AM $$= 13 - 4= 9 \\, (cm)$<br\/>X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $ C$, \u0111\u01b0\u1eddng cao $CM$ c\u00f3: <br\/> $CM^2=AM.MB$ (H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow CM^2 =9.4=36$ <br\/> $\\Rightarrow CM = 6\\, (cm) $ <br\/> $\\Rightarrow CD = 2CM =2. 6 = 12\\, (cm)$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12.$ <\/span><\/span>"}]}],"id_ques":1119},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $MNP$ c\u00e2n t\u1ea1i $M$ c\u00f3 c\u1ea1nh b\u00ean b\u1eb1ng $6 cm$ v\u00e0 g\u00f3c \u1edf \u0111\u1ec9nh b\u1eb1ng $120^o$. 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. $6\\,cm$","B. $\\dfrac{3\\sqrt{3}}{2}\\,cm$","C. $3\\sqrt{3}\\,cm$","D. $\\sqrt{3}\\,cm$"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn <\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> V\u1ebd th\u00eam h\u00ecnh \u0111\u1ec3 t\u00ecm t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp $\\Delta MNP$ <br\/><b> B\u01b0\u1edbc 2: <\/b> \u00c1p d\u1ee5ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn \u0111\u1ec3 t\u00ednh b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp $\\Delta MNP$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai6/lv3/img\/H921_K1.jpg' \/><\/center> K\u1ebb $MH \\bot NP $ t\u1ea1i $H$ <br\/> $\\Rightarrow MH$ l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a $\\widehat{NMP}$ ($\\Delta MNP$ c\u00e2n) <br\/> $\\Rightarrow \\widehat{NMH}=\\widehat{HMP}={{60}^{o}}$ <br\/> Qua trung \u0111i\u1ec3m $I$ c\u1ee7a $MN$ k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi $MN$ c\u1eaft $MH$ t\u1ea1i $O$<br\/>Suy ra $O$ l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c $MNP$ v\u00e0 c\u00f3 b\u00e1n k\u00ednh l\u00e0 $OM$ <br\/>X\u00e9t $\\Delta OIM $ c\u00f3: <br\/> $\\widehat{MIO}=90^o$; $IM=\\dfrac{MN}{2}=3\\,cm$ <br\/> $cos \\widehat{OMI} = \\dfrac{IM}{OM}$ (t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow OM=\\dfrac{IM}{\\cos \\widehat{OMI}} $ <br\/>$\\Rightarrow OM=\\dfrac{3}{\\cos 60^o}=6 \\,(cm)$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span><\/span>","column":4}]}],"id_ques":1120}],"lesson":{"save":0,"level":3}}