{"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":[[["2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, $AB=\\sqrt{5} (cm),\\,AC=2\\sqrt{5} (cm)$<br\/>\u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao $AH$ l\u00e0: _input_ (cm)<\/span> ","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}\\,$ ","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D22.png' \/><\/center> X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$, $AH\\bot BC$. <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n v\u00e0 hai c\u1ea1nh g\u00f3c vu\u00f4ng trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3: <br\/> $\\dfrac{1}{AH^2}=\\dfrac{1}{AB^2}+\\dfrac{1}{AC^2}\\\\ \\Rightarrow \\dfrac{1}{AH^2}=\\dfrac{1}{5}+\\dfrac{1}{20}\\\\ \\Rightarrow \\dfrac{1}{AH^2}=\\dfrac{1}{4}\\\\\\Rightarrow AH^2=4\\\\ \\Rightarrow AH= 2$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2$.<\/span><\/span>"}]}],"id_ques":1281},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang \u0111\u1ec3 \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, _______ \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng _______ hai h\u00ecnh chi\u1ebfu c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n. ","select":["A. l\u1eadp ph\u01b0\u01a1ng , t\u00edch","B. b\u00ecnh ph\u01b0\u01a1ng, t\u00edch ","C. \u0111\u1ed9 d\u00e0i, t\u1ed5ng","D. b\u00ecnh ph\u01b0\u01a1ng, t\u1ed5ng"],"explain":" Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, <b> b\u00ecnh ph\u01b0\u01a1ng <\/b> \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng <b> t\u00edch <\/b> hai h\u00ecnh chi\u1ebfu c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span>","column":2}]}],"id_ques":1282},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\dfrac{144}{13}$","B. $\\dfrac{140}{3}$","C. $\\dfrac{145}{3}$"],"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D13.png' \/><\/center> <br\/> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. Bi\u1ebft $AB= 12 cm$; $BC= 13 cm$ <br\/> \u0110\u1ed9 d\u00e0i c\u1ea1nh $BH$ l\u00e0 ? $(cm)$","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D13.png' \/><\/center><span class='basic_left'> X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$, $AH\\bot BC$. <br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n, ta c\u00f3: <br\/> $AB^2=BH.BC\\,$ <br\/> $\\Rightarrow BH=\\dfrac{AB^2}{BC}\\,$$=\\dfrac{144}{13}\\,(cm)$<\/span>"}]}],"id_ques":1283},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ecm $x$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D12.png'\/><center> <br\/>\u0110\u00e1p s\u1ed1: $x=$ _input_","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=b'.a;\\,\\,c^2=c'.a$","explain":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n, ta c\u00f3: <br\/> $4^2=x.3,2$$ \\Rightarrow x=\\dfrac{16}{3,2}$$\\Rightarrow x=5$ <br\/> <span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $5$.<\/span>"}]}],"id_ques":1284},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\dfrac{60}{13}$","B. $\\dfrac{64}{13}$","C. $\\dfrac{54}{13}$"],"ques":"T\u00ecm $x$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D5.png'\/><center> <br\/>\u0110\u00e1p s\u1ed1: $x=$ ?","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{b^2}+\\dfrac{1}{c^2}$","explain":"<span class='basic_left'>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n v\u00e0 hai c\u1ea1nh g\u00f3c vu\u00f4ng trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3: <br\/> $\\dfrac{1}{x^2}=\\dfrac{1}{12^2}+\\dfrac{1}{5^2}\\\\ \\Rightarrow \\dfrac{1}{x^2}=\\dfrac{169}{3600}\\\\ \\Rightarrow x=\\dfrac{60}{13}$<\/span>"}]}],"id_ques":1285},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho ba c\u00e2u","temp":"fill_the_blank","correct":[[["15"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, bi\u1ebft $AH \\bot BC$ t\u1ea1i $H$, $BH= 9 cm $ v\u00e0 $ CH = 16 cm$. <br\/><b> C\u00e2u 1: <\/b> \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng $AB$ l\u00e0: _input_ $(cm)$<\/span>","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=a.b'; c^2=a.c'$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D6.png' \/><\/center><br\/> <span class='basic_left'> Ta c\u00f3: $BC= BH + CH= 9+ 16$$= 25\\, (cm)$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n trong $\\Delta ABC$ , ta c\u00f3: <br\/>$AB^2=BH. BC\\\\ \\Rightarrow AB^2=9.25=225\\\\ \\Rightarrow AB= 15 \\,(cm)$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $15$.<\/span> <\/span><\/span>"}]}],"id_ques":1286},{"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 ba c\u00e2u","temp":"fill_the_blank","correct":[[["12"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, bi\u1ebft $AH \\bot BC$ t\u1ea1i $H$, $ BH= 9 cm $ v\u00e0 $ CH = 16 cm$. <br\/><b> C\u00e2u 2: <\/b> \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng $AH$ l\u00e0: _input_ $(cm)$<\/span>","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $h^2=b'.c'$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D6.png' \/><\/center><br\/>Ta c\u00f3 $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$, $AH \\bot BC$ t\u1ea1i $H$ <br\/> $\\Rightarrow AH^2 =BH.HC\\,\\,$ (h\u1ec7 th\u1ee9c li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AH= \\sqrt{9.16}=12\\,(cm)$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12$.<\/span><\/span>"}]}],"id_ques":1287},{"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 ba c\u00e2u","temp":"fill_the_blank","correct":[[["60"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, bi\u1ebft $\\,AH \\bot BC$ t\u1ea1i $H,$ $BH= 9 cm$ v\u00e0 $CH = 16 cm$ <br\/><b> C\u00e2u 3: <\/b>Chu vi tam gi\u00e1c $ABC$ l\u00e0: _input_ $(cm)$ <\/span>","hint":"T\u00ednh c\u1ea1nh $AC$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D6.png' \/><\/center><br\/> <span class='basic_left'>Theo c\u00e2u 1, ta c\u00f3: $BC=25\\,(cm),\\,AB=15\\,(cm)$ <br\/> Ta c\u00f3: $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> $\\Rightarrow AC^2=HC.BC\\,\\,$ (h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AC= \\sqrt{16.25}=20\\,(cm)$ <br\/> Chu vi tam gi\u00e1c $ABC$ l\u00e0: <br\/> $AB+AC+BC\\,$$=15+20+25=60\\,(cm)$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $60$<\/span><\/span><\/span>"}]}],"id_ques":1288},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $AC^2$","B. $2AC$","C. $2AC^2$"],"ques":"Ho\u00e0n th\u00e0nh bi\u1ec3u th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng, c\u1ea1nh huy\u1ec1n v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n: <center> <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D1.png' \/><center> $BC.CH=$ ?","explain":"<span class='basic_left'>Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n: $BC.CH=AC^2$ "}]}],"id_ques":1289},{"time":24,"part":[{"time":3,"title":"H\u00e3y gh\u00e9p m\u1ed7i \u00f4 \u1edf c\u1ed9t tr\u00e1i v\u1edbi m\u1ed9t \u00f4 \u1edf c\u1ed9t ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c m\u1ed9t kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang","title_trans":"","audio":"","temp":"matching","correct":[["3","1","2"]],"list":[{"point":5,"image":"","left":["Trong tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng","Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng","Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, t\u00edch hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng"],"right":["t\u00edch hai h\u00ecnh chi\u1ebfu c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n","t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng","t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n"],"top":100,"explain":"<span class='basic_left'>Trong tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n <br\/> Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng t\u00edch hai h\u00ecnh chi\u1ebfu c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n <br\/>Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, t\u00edch hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng t\u00edch c\u1ee7a c\u1ea1nh huy\u1ec1n v\u00e0 \u0111\u01b0\u1eddng cao t\u01b0\u01a1ng \u1ee9ng.<\/span>"}]}],"id_ques":1290},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["BH","HB"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Ho\u00e0n th\u00e0nh bi\u1ec3u th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa hai h\u00ecnh chi\u1ebfu c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n v\u00e0 \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D1.png' \/><center>$AH^2=CH.$ _input_","explain":"<span class='basic_left'>Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng t\u00edch hai h\u00ecnh chi\u1ebfu c\u1ee7a hai c\u1ea1nh g\u00f3c vu\u00f4ng tr\u00ean c\u1ea1nh huy\u1ec1n: <br\/> $AH^2=CH.HB$ <br\/> <span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $BH$. <\/span>"}]}],"id_ques":1291},{"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":[[["7,5"],["10"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"T\u00ecm $x$ v\u00e0 $y$ trong h\u00ecnh v\u1ebd sau: <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D10.png' \/><center> \u0110\u00e1p s\u1ed1: $x=$ _input_ ; $\\,\\,y=$ _input_ <br\/> (Vi\u1ebft k\u1ebft qu\u1ea3 d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n)","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}\\,$ v\u00e0 \u0111\u1ecbnh l\u00fd Pytago","explain":"<span class='basic_left'> X\u00e9t $\\Delta ABH$ c\u00f3: $\\widehat{H}={{90}^{o}}$ (gi\u1ea3 thi\u1ebft) <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago ta c\u00f3: <br\/> $AB^2=BH^2+AH^2\\,$$=6^2+4,5^2=56,25 \\,$ <br\/> $\\Rightarrow x=7,5$ <br\/>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}; AH \\bot BC$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n v\u00e0 hai c\u1ea1nh g\u00f3c vu\u00f4ng trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3:<br\/>$\\begin{align}\\dfrac{1}{AH^2}=\\dfrac{1}{AB^2}+\\dfrac{1}{AC^2} \\\\\\Rightarrow & \\dfrac{1}{6^2}=\\dfrac{1}{7,5^2}+\\dfrac{1}{AC^2}\\\\ \\Rightarrow &AC^2=100\\\\\\Rightarrow &y=AC = 10\\end{align}$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $7,5$ v\u00e0 $10$.<\/span> <\/span>"}]}],"id_ques":1292},{"time":24,"part":[{"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":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. G\u1ecdi $M$ v\u00e0 $N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a $H$ tr\u00ean $AB$ v\u00e0 $AC$. <br\/> <b> C\u00e2u 1:<\/b> T\u1ee9 gi\u00e1c $AMHN$ l\u00e0 h\u00ecnh g\u00ec?<\/span> ","select":["A. H\u00ecnh vu\u00f4ng","B. H\u00ecnh thoi ","C. H\u00ecnh ch\u1eef nh\u1eadt"],"explain":"<span class='basic_left'> <center><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D14.png' \/><\/center> <br\/> X\u00e9t t\u1ee9 gi\u00e1c $AMHN$ ta c\u00f3: $\\widehat{A}=\\widehat{M}=\\widehat{N}=90^{o}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow$ T\u1ee9 gi\u00e1c $AMHN$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span> <\/span>","column":3}]}],"id_ques":1293},{"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 b\u1ed1n c\u00e2u ","temp":"fill_the_blank","correct":[[["AB","BA"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":" <span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. G\u1ecdi $M$ v\u00e0 $N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a $H$ tr\u00ean $AB$ v\u00e0 $AC$. <br\/> <b> C\u00e2u 2: <\/b> Khi \u0111\u00f3 ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c $AH^2=AM.\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ <\/span> ","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=b'.a;\\,\\,c^2=c'.a$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D14.png' \/><\/center> <br\/>X\u00e9t $\\Delta AHB$ c\u00f3: $\\widehat{AHB}=90^{o}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\, HM\\bot AB$ t\u1ea1i $M$ (gi\u1ea3 thi\u1ebft) <br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n trong tam gi\u00e1c vu\u00f4ng $AHB$. <br\/> $\\Rightarrow AH^2= AM. AB $ <br\/> <span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $AB$. <\/span><\/span>"}]}],"id_ques":1294},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $>, < , =$ th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho b\u1ed1n c\u00e2u","temp":"fill_the_blank","correct":[[["="]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. G\u1ecdi $M$ v\u00e0 $N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a $H$ tr\u00ean $AB$ v\u00e0 $AC$. <br\/><b> C\u00e2u 3:<\/b>So s\u00e1nh $AM.AB$ v\u00e0 $AN.AC$ <br\/><b> \u0110\u00e1p s\u1ed1:<\/b> $AM.AB$ _input_ $AN.AC$ ","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=b'.a;\\,\\,c^2=c'.a$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D14.png' \/><\/center> <br\/>X\u00e9t $\\Delta AHC$ c\u00f3: $\\widehat{AHC}=90^{o}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\, HN\\bot AC$ <br\/> $\\Rightarrow AH^2= AN. AC $ (h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 tr\u00ean c\u1ea1nh huy\u1ec1n) <br\/> Theo c\u00e2u 2 tr\u00ean, ta c\u00f3 $\\,AM.AB=AH^2$ <br\/> $\\Rightarrow AM.AB=AN.AC=AH^2$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $=$. <\/span> <\/span>"}]}],"id_ques":1295},{"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 b\u1ed1n c\u00e2u","temp":"fill_the_blank","correct":[[["4,8"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'> Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. G\u1ecdi $M$ v\u00e0 $N$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a $H$ tr\u00ean $AB$ v\u00e0 $AC$. <br\/> <b> C\u00e2u 4:<\/b> V\u1edbi $BH= 6$; $AH= 8$. \u0110\u1ed9 d\u00e0i $MH$ l\u00e0: _input_<br\/> (K\u1ebft qu\u1ea3 vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n) ","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D14.png' \/><\/center> <br\/> X\u00e9t $\\Delta AHB$ c\u00f3: $\\widehat{AHB}=90^{o};$$\\, HM\\bot AB$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh v\u00e0 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng $ABH$, ta c\u00f3: <br\/> $\\begin {align}&\\dfrac{1}{MH^2}= \\dfrac{1}{BH^2}+\\dfrac{1}{AH^2}\\\\ \\Rightarrow &\\dfrac{1}{MH^2}=\\dfrac{1}{6^2}+\\dfrac{1}{8^2}\\\\ \\Rightarrow & MH=4,8 \\end{align} $ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4,8$.<\/span> <\/span>"}]}],"id_ques":1296},{"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":[[["6"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $AH$. H\u1ea1 $HE \\,\\bot\\, AB$, $HF \\,\\bot\\, AC$ ($E \\,\\in\\, AB$; $F \\,\\in\\, AC$). Bi\u1ebft $BH = 4cm$ v\u00e0 $CH= 9cm$. Khi \u0111\u00f3, \u0111\u1ed9 d\u00e0i $EF$ l\u00e0: _input_ $(cm)$ ","hint":"Ch\u1ee9ng minh $EF = AH$","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 $AEHF$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt <br\/><b> B\u01b0\u1edbc 2: <\/b> T\u00ednh c\u1ea1nh $AH$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D19.png' \/><\/center> X\u00e9t t\u1ee9 gi\u00e1c $AEHF$ c\u00f3: $\\widehat{A}=\\widehat{E}=\\widehat{F}=90^{o}$ <br\/> Suy ra, t\u1ee9 gi\u00e1c $AEHF$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft) <br\/> $\\Rightarrow EF= AH\\,\\,\\text{(t\u00ednh ch\u1ea5t)}$<br\/>X\u00e9t $\\Delta ABC$ c\u00f3:$ \\widehat{A}=90^{o}; AH\\bot BC$<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam vu\u00f4ng $ABC$, ta c\u00f3:<br\/>$ AH^2=BH.CH=4.9=36\\\\ \\Rightarrow AH = EF= 6 \\,(cm) $ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6$.<\/span>"}]}],"id_ques":1297},{"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":[[["18"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D18.png' \/><\/center> <br\/> Cho tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$, \u0111\u01b0\u1eddng cao $\\,AH=3\\sqrt{2}cm\\,$<br\/>Di\u1ec7n t\u00edch tam gi\u00e1c $ABC$ l\u00e0 _input_ $(cm^2)$","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}$ \u0111\u1ec3 t\u00ednh $AB$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D18.png' \/><\/center>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o},$ $\\,\\,AH\\bot BC, \\, AB=AC$.<br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh v\u00e0 \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3: <br\/> $\\dfrac{1}{AH^2}=\\dfrac{1}{AB^2}+\\dfrac{1}{AC^2}\\,$ <br\/> $\\Rightarrow \\dfrac{1}{18}=\\dfrac{2}{AB^2}\\,$$\\Rightarrow AB=AC= 6\\,(cm)$ <br\/> Di\u1ec7n t\u00edch tam gi\u00e1c $ABC$ l\u00e0: <br\/> $\\dfrac{AB.AC}{2}=\\dfrac{6.6}{2}\\,$$=18\\,(cm^2)$ <br\/> <span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $18$.<\/span><\/span>"}]}],"id_ques":1298},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $6\\sqrt{2}$","B. $7\\sqrt{2}$","C. $8\\sqrt{2}$"],"ques":"Tam gi\u00e1c $PQR$ vu\u00f4ng t\u1ea1i $P$, c\u00f3 \u0111\u01b0\u1eddng cao $PH= 4 \\,cm$ v\u00e0 $\\dfrac{QH}{HR}=\\dfrac{1}{2}$<br\/>\u0110\u1ed9 d\u00e0i \u0111o\u1ea1n $QR$ l\u00e0 ?$(cm)$ ","hint":"\u0110\u1eb7t $QH=x; HR=2x$. Sau \u0111\u00f3, \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c $h^2=b'.c'$","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D20.png' \/><\/center> Ta c\u00f3: $\\dfrac{QH}{HR}=\\dfrac{1}{2}$$\\,\\Rightarrow \\dfrac{QH}{1}=\\dfrac{HR}{2}=x$ <br\/> Suy ra $QH= x; HR= 2x$ <br\/> X\u00e9t $\\Delta PQR$ vu\u00f4ng t\u1ea1i $P$ c\u00f3 $PH\\bot QR$.<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng cao trong tam gi\u00e1c vu\u00f4ng $PQR$, ta c\u00f3: <br\/> $ PH^2=QH.HR\\\\ \\Rightarrow 4^2 = x.2x \\\\ \\Rightarrow x= \\sqrt{8}$ <br\/> Khi \u0111\u1edb $QR = QH + HR $$=3x$ $= 3\\sqrt{8}=6\\sqrt{2}\\,(cm)$ <br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6\\sqrt{2}$. <\/span><\/span>"}]}],"id_ques":1299},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7,2"],["12,8"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ecm $x$ v\u00e0 $y$ trong h\u00ecnh v\u1ebd sau: <center> <img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai1/lv1/img\/H911_D7.png' \/><center> <br\/>\u0110\u00e1p s\u1ed1: $x=$ _input_; $\\,\\,y=$_input_<br\/>(Vi\u1ebft k\u1ebft qu\u1ea3 d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n)","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=a.b'; c^2=a.c'$","explain":"<span class='basic_left'> \u0110\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n l\u00e0 $x +y = 20$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $b^2=a.b'$, ta \u0111\u01b0\u1ee3c: <br\/> $12^2=20.x\\,$ <br\/> $\\Leftrightarrow x= \\dfrac{12^2}{20}=7,2$ <br\/> $\\Rightarrow y= 20 - x \\,$$= 20 - 7,2=12,8$ <br\/> <span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $7,2$ v\u00e0 $12,8$.<\/span>"}]}],"id_ques":1300}],"lesson":{"save":0,"level":1}}