{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","temp":"fill_the_blank","correct":[[["12,5"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ v\u00e0 d\u00e2y $AB, \\,C$ l\u00e0 \u0111i\u1ec3m ch\u00ednh gi\u1eefa cung $AB,\\, M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a d\u00e2y $AB.$ T\u00ednh b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ bi\u1ebft $AB= 24 cm,\\, CM= 9cm.$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> B\u00e1n k\u00ednh \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/bai14/lv3/img\/h932_K1.png' \/><\/center> <br\/> K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $CD$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O)$ <br\/> Do $\\overset\\frown{AC}=\\overset\\frown{BC}\\Rightarrow AC = BC$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 cung) <br\/> $\\Rightarrow C$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> M\u00e0 $MA=MB = 12 cm \\Rightarrow M$ thu\u1ed9c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a $AB$ <br\/> $\\Rightarrow CM$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AB$ <br\/> M\u00e0 $CD$ l\u00e0 trung tr\u1ef1c c\u1ee7a $AB$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow C,\\, M,\\, D$ th\u1eb3ng h\u00e0ng <br\/> $\\Rightarrow CD\\bot AB$ <br\/> X\u00e9t $\\Delta CBD$ c\u00f3: <br\/> $OB=OC=OD=R$ <br\/> $\\Rightarrow \\Delta CBD$ vu\u00f4ng t\u1ea1i $B$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow M{{B}^{2}}=CM.MD$ (h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow MD=\\dfrac{M{{B}^{2}}}{CM} = \\dfrac{{{12}^{2}}}{9}=16\\,\\,\\left( cm \\right)$ <br\/> $\\Rightarrow R=\\dfrac{CD}{2}=\\dfrac{\\left( CM+MD \\right)}{2}=\\dfrac{9+16}{2}=12,5\\,\\,\\left( cm \\right)$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12,5$ <\/span><\/span> "}]}],"id_ques":1461},{"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 $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O\u2019)$ \u0111\u01b0\u1eddng k\u00ednh $AO.$ L\u1ea5y c\u00e1c \u0111i\u1ec3m $C, D$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n $(O)$ sao cho $B\\in \\overset\\frown{CD}$ , $\\overset\\frown{BC}<\\overset\\frown{BD}$ . C\u00e1c d\u00e2y $AC,\\, AD$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n $(O\u2019)$ theo th\u1ee9 t\u1ef1 $E$ v\u00e0 $F$. <br\/> <b> C\u00e2u 1: <\/b> So s\u00e1nh \u0111\u1ed9 d\u00e0i $OE$ v\u00e0 $OF$<br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $OE$ _input_ $OF$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K2.png' \/><\/center> <br\/> X\u00e9t $\\Delta AEO$ c\u00f3: <br\/> $O'A=O'E=O'O$ (c\u00f9ng b\u1eb1ng b\u00e1n k\u00ednh c\u1ee7a $(O\u2019)$) <br\/> $\\Rightarrow \\Delta AEO$ vu\u00f4ng t\u1ea1i $E$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow OE\\bot AC$ <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: $OF \\bot AD $ <br\/> Trong $(O)$ ta c\u00f3: <br\/> $OE\\bot AC \\Rightarrow AE=EC$ (quan h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $OF\\bot AD \\Rightarrow AF = FD$ (quan h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> $\\Rightarrow OE$ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a $\\Delta ABC$ <br\/> $\\Rightarrow OE=\\dfrac{1}{2}BC$ (1) <br\/> T\u01b0\u01a1ng t\u1ef1: $OF=\\dfrac{1}{2}BD$ (2) <br\/> Ta c\u00f3 $\\overset\\frown{BC} < \\overset\\frown{BD} \\Rightarrow BC < BD$ (\u0111\u1ecbnh l\u00fd li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) (3) <br\/> T\u1eeb (1), (2) v\u00e0 (3) $\\Rightarrow OE < OF$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $<$ <\/span><\/span> "}]}],"id_ques":1462},{"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 $(O)$ \u0111\u01b0\u1eddng k\u00ednh $AB$ v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n $(O\u2019)$ \u0111\u01b0\u1eddng k\u00ednh $AO.$ L\u1ea5y c\u00e1c \u0111i\u1ec3m $C, D$ thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n $(O)$ sao cho $B\\in \\overset\\frown{CD}$ , $\\overset\\frown{BC}<\\overset\\frown{BD}$ . C\u00e1c d\u00e2y $AC, \\,AD$ c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n $(O\u2019)$ theo th\u1ee9 t\u1ef1 $E$ v\u00e0 $F$. <br\/> <b> C\u00e2u 2: <\/b> So s\u00e1nh c\u00e1c cung $ AE, \\,AF$ c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O\u2019)$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $\\overset\\frown{AE}$ _input_ $\\overset\\frown{AF}$","explain":" <span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K2.png' \/><\/center> <br\/> Trong $(O\u2019)$, ta c\u00f3: <br\/> $\\overset\\frown{AE}+\\overset\\frown{EO}=\\overset\\frown{\\text{OF}}+\\overset\\frown{\\text{AF}}$ (c\u00f9ng b\u1eb1ng n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n) <br\/> M\u00e0 $OE < OF$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\overset\\frown{EO} < \\overset\\frown{OF}$ (\u0111\u1ecbnh l\u00fd li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> Suy ra $\\overset\\frown{AE} > \\overset\\frown{AF}$ <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 $>$ <\/span><\/span> "}]}],"id_ques":1463},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ hai d\u00e2y $AB, CD$ vu\u00f4ng g\u00f3c v\u1edbi nhau t\u1ea1i $I\\, (C$ thu\u1ed9c cung nh\u1ecf $AB).$ K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $BE.$ <br\/> <b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh r\u1eb1ng $AC=DE$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[3],[5],[1],[4]]],"list":[{"point":10,"left":["$\\Rightarrow \\Delta AEB$ vu\u00f4ng t\u1ea1i $A$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AE\\bot AB$ ","M\u00e0 $CD\\bot AB$ $\\Rightarrow AE\/\/CD$ (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song)"," $\\Rightarrow AC=ED$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) "," X\u00e9t $\\Delta AEB$ c\u00f3: $OA=OE=OB=R$ "," $\\Rightarrow \\overset\\frown{AC}=\\overset\\frown{ED}$ (hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K4.png' \/><\/center> <br\/> X\u00e9t $\\Delta AEB$ c\u00f3: <br\/> $OA=OE=OB=R$ <br\/> $\\Rightarrow \\Delta AEB$ vu\u00f4ng t\u1ea1i $A$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AE\\bot AB$ <br\/> M\u00e0 $CD\\bot AB$ $\\Rightarrow AE\/\/CD$ (t\u1eeb vu\u00f4ng g\u00f3c \u0111\u1ebfn song song) <br\/> $\\Rightarrow \\overset\\frown{AC}=\\overset\\frown{ED}$ (hai cung b\u1ecb ch\u1eafn gi\u1eefa hai d\u00e2y song song) <br\/> $\\Rightarrow AC=ED$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <\/span>"}]}],"id_ques":1464},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["frac"],"ques":" <span class='basic_left'> Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; R)$ hai d\u00e2y $AB, CD$ vu\u00f4ng g\u00f3c v\u1edbi nhau t\u1ea1i $I\\, (C$ thu\u1ed9c cung nh\u1ecf $AB).$ K\u1ebb \u0111\u01b0\u1eddng k\u00ednh $BE.$ <br\/> <b> C\u00e2u 2: <\/b> Khi \u0111\u00f3, ta c\u00f3: $I{{A}^{2}}+I{{B}^{2}}+I{{C}^{2}}+I{{D}^{2}}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}{{R}^{2}}$ ","explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K5.png' \/><\/center> <br\/><br\/> X\u00e9t $\\Delta AIC$ vu\u00f4ng t\u1ea1i $I$ c\u00f3: <br\/> $I{{A}^{2}}+I{{C}^{2}}=A{{C}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> Ta c\u00f3: $AC =DE$ (theo c\u00e2u 1) <br\/> $\\Rightarrow I{{A}^{2}}+I{{C}^{2}}=D{{E}^{2}}$ (1) <br\/> X\u00e9t $\\Delta BID$ vu\u00f4ng t\u1ea1i $I$ c\u00f3: <br\/> $I{{B}^{2}}+I{{D}^{2}}=B{{D}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) (2) <br\/> X\u00e9t $\\Delta BED$ c\u00f3: $OB=OD=OE=R$ <br\/> $\\Rightarrow \\Delta BED$ vu\u00f4ng t\u1ea1i $D$ <br\/> $\\Rightarrow D{{E}^{2}}+D{{B}^{2}}=B{{E}^{2}}={{\\left( 2R \\right)}^{2}}=4{{R}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) (3) <br\/> T\u1eeb (1), (2) v\u00e0 (3), suy ra $I{{A}^{2}}+I{{B}^{2}}+I{{C}^{2}}+I{{D}^{2}}=4{{R}^{2}}$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4$<\/span> <\/span>"}]}],"id_ques":1465},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Qua \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O),$ v\u1ebd hai c\u00e1t tuy\u1ebfn $MAB$ v\u00e0 $MCD$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n sao cho $AB > CD.$ G\u1ecdi $H$ v\u00e0 $K$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $CD.$ <br\/> <b> C\u00e2u 1: <\/b> Ch\u1ee9ng minh $MH > MK$ ","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],[6],[1],[4],[2]]],"list":[{"point":10,"left":["X\u00e9t $\\Delta OMH$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: $M{{H}^{2}}+O{{H}^{2}}=O{{M}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) (1) ","T\u1eeb (1) v\u00e0 (2) $\\Rightarrow M{{H}^{2}}+O{{H}^{2}}=O{{K}^{2}}+M{{K}^{2}}$ "," Do $OH < OK$ (ch\u1ee9ng minh tr\u00ean) $\\Rightarrow MH > MK$ "," Ta c\u00f3: $AH=HB, CK=CD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow $ $OH\\bot AB;\\,OK\\bot CD$ (quan h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) "," X\u00e9t $\\Delta OKM$ vu\u00f4ng t\u1ea1i $K$ c\u00f3: $O{{K}^{2}}+M{{K}^{2}}=O{{M}^{2}}$(\u0111\u1ecbnh l\u00ed Pitago) (2) "," M\u00e0 $AB > CD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow OH < OK$ (li\u00ean h\u1ec7 gi\u1eefa d\u00e2y cung v\u00e0 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn t\u00e2m) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K6.png' \/><\/center> <br\/> Ta c\u00f3: $AH=HB, CK=CD$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow $ $OH\\bot AB;\\,OK\\bot CD$ (quan h\u1ec7 gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> M\u00e0 $AB > CD$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow OH < OK$ (li\u00ean h\u1ec7 gi\u1eefa d\u00e2y cung v\u00e0 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn t\u00e2m) <br\/> X\u00e9t $\\Delta OMH$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $M{{H}^{2}}+O{{H}^{2}}=O{{M}^{2}}$ (\u0111\u1ecbnh l\u00ed Pitago) (1) <br\/> X\u00e9t $\\Delta OKM$ vu\u00f4ng t\u1ea1i $K$ c\u00f3: <br\/> $O{{K}^{2}}+M{{K}^{2}}=O{{M}^{2}}$(\u0111\u1ecbnh l\u00ed Pitago) (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow M{{H}^{2}}+O{{H}^{2}}=O{{K}^{2}}+M{{K}^{2}}$ <br\/> Do $OH < OK$ (ch\u1ee9ng minh tr\u00ean) $\\Rightarrow MH > MK$ <\/span>"}]}],"id_ques":1466},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Qua \u0111i\u1ec3m $M$ n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n $(O),$ v\u1ebd hai c\u00e1t tuy\u1ebfn $MAB$ v\u00e0 $MCD$ v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n sao cho $AB > CD.$ G\u1ecdi $H$ v\u00e0 $K$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ v\u00e0 $CD.$ <br\/> <b> C\u00e2u 2: <\/b> Ch\u1ee9ng minh $\\widehat{MOH}>\\widehat{MOK}$","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh ","temp":"sequence","correct":[[[4],[1],[5],[3],[6],[2]]],"list":[{"point":10,"left":[" $\\Rightarrow IM=IO=IH=IK$ <br\/> $\\Rightarrow H,M,K,O$ c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n $(I)$ ","G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MO$. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $(I; IO)$ "," Trong \u0111\u01b0\u1eddng tr\u00f2n $(I)$, ta c\u00f3: $MH > MK$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\overset\\frown{MH}>\\overset\\frown{MK}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) "," Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 $\\Rightarrow IK=IM=IO$ "," Hay $\\text{s\u0111}\\overset\\frown{MH}>\\text{s\u0111}\\overset\\frown{MK}$ $\\Rightarrow \\widehat{MIH}=\\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{MH}>\\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{MH}=\\widehat{MIK}$ (\u0111\u1ecbnh l\u00ed g\u00f3c n\u1ed9i ti\u1ebfp) ","X\u00e9t $\\Delta MHO$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: $IO=IM$ (c\u00e1ch d\u1ef1ng) <br\/> $\\Rightarrow IO=IM=IH$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng)"],"top":100,"hint":"G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MO$. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $(I; IO)$ r\u1ed3i ch\u1ee9ng minh $\\text{s\u0111}\\overset\\frown{MH}>\\text{s\u0111}\\overset\\frown{MK}$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K7.png' \/><\/center> <br\/> G\u1ecdi $I$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $MO$. V\u1ebd \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $(I; IO)$ <br\/> X\u00e9t $\\Delta MHO$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $IO=IM$ (c\u00e1ch d\u1ef1ng) <br\/> $\\Rightarrow IO=IM=IH$ (t\u00ednh ch\u1ea5t trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng) <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 $\\Rightarrow IK=IM=IO$ <br\/> $\\Rightarrow IM=IO=IH=IK$ <br\/> $\\Rightarrow H,M,K,O$ c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n $(I)$ <br\/> Trong \u0111\u01b0\u1eddng tr\u00f2n $(I)$, ta c\u00f3: <br\/> $MH > MK$ (theo c\u00e2u 1) <br\/> $\\Rightarrow \\overset\\frown{MH}>\\overset\\frown{MK}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y) <br\/> Hay $\\text{s\u0111}\\overset\\frown{MH}>\\text{s\u0111}\\overset\\frown{MK}$ <br\/> $\\Rightarrow \\widehat{MIH}=\\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{MH}>\\dfrac{1}{2}\\text{s\u0111}\\overset\\frown{MH}=\\widehat{MIK}$ (\u0111\u1ecbnh l\u00ed g\u00f3c n\u1ed9i ti\u1ebfp) <\/span>"}]}],"id_ques":1467},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'> Cho h\u00ecnh v\u1ebd sau, <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K8.png' \/><\/center> <br\/> Trong \u0111\u00f3, $MN = PQ$. Ch\u1ee9ng minh r\u1eb1ng $AN = AQ$","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],[2],[6],[4]]],"list":[{"point":10,"left":[" $\\Rightarrow \\Delta OEA=\\Delta OFA$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow AE=AF$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) ","M\u00e0 $MN = PQ$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow EN=FQ$ "," Ta c\u00f3: $MN=PQ\\Rightarrow OE=OF$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) "," X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OEA$ v\u00e0 $\\Delta OFA$ c\u00f3: $\\left\\{ \\begin{align} & OE=OF\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & OA\\,\\text{chung} \\\\ \\end{align} \\right.$ "," $\\Rightarrow AE-EN=AQ-FQ\\,hay\\,AN=AQ$ ","V\u00ec $\\left\\{ \\begin{align} & OE\\bot MN \\\\ & OF\\bot PQ \\\\ \\end{align} \\right.$$\\Rightarrow \\left\\{ \\begin{align} & ME=EN \\\\ & PF=FQ \\\\ \\end{align} \\right.$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K8.png' \/><\/center> <br\/> Ta c\u00f3: $MN=PQ$ <br\/> $\\Rightarrow OE=OF$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OEA$ v\u00e0 $\\Delta OFA$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & OE=OF\\,\\left(\\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & OA\\,\\text{chung} \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta OEA=\\Delta OFA$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow AE=AF$ (hai c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng) <br\/> V\u00ec $\\left\\{ \\begin{align} & OE\\bot MN \\\\ & OF\\bot PQ \\\\ \\end{align} \\right.$$\\Rightarrow \\left\\{ \\begin{align} & ME=EN \\\\ & PF=FQ \\\\ \\end{align} \\right.$ (\u0111\u1ecbnh l\u00ed \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> M\u00e0 $MN = PQ$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow EN=FQ$ <br\/> $\\Rightarrow AE-EN=AF-FQ$ hay $AN=AQ$ <\/span>"}]}],"id_ques":1468},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O)$, hai d\u00e2y $AB, CD$ b\u1eb1ng nhau v\u00e0 c\u1eaft nhau t\u1ea1i \u0111i\u1ec3m $I$ n\u1eb1m trong \u0111\u01b0\u1eddng tr\u00f2n. Ch\u1ee9ng minh r\u1eb1ng $OI$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t trong hai g\u00f3c t\u1ea1o b\u1edfi hai d\u00e2y $AB$ v\u00e0 $CD$ ","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c b\u00e0i ch\u1ee9ng minh","temp":"sequence","correct":[[[2],[4],[5],[6],[3],[1]]],"list":[{"point":10,"left":[" V\u00ec $AB=CD\\Rightarrow OH=OK$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) ","$\\left\\{ \\begin{align} & OH=OK\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & OI\\,\\text{chung} \\\\ \\end{align} \\right.$ "," $\\Rightarrow \\Delta OHI=\\Delta OKI$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{OIH}=\\widehat{OIK}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) "," $\\Rightarrow OI$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c t\u1ea1o th\u00e0nh b\u1edfi hai d\u00e2y $AB$ v\u00e0 $CD$ "," X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OHI$ v\u00e0 $\\Delta OKI$ c\u00f3: ","K\u1ebb c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $OH\\bot AB;\\,OK\\bot CD$ "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K9.png' \/><\/center> <br\/> K\u1ebb c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng $OH\\bot AB;\\,OK\\bot CD$ <br\/> V\u00ec $AB=CD \\Rightarrow OH=OK$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OHI$ v\u00e0 $\\Delta OKI$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & OH=OK\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ & OI\\,\\text{chung} \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta OHI=\\Delta OKI$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{OIH}=\\widehat{OIK}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\Rightarrow OI$ l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c t\u1ea1o th\u00e0nh b\u1edfi hai d\u00e2y $AB$ v\u00e0 $CD$ <\/span>"}]}],"id_ques":1469},{"time":24,"part":[{"time":3,"title":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O;R)$ v\u00e0 c\u00e1c b\u00e1n k\u00ednh $OA; OB$. Tr\u00ean cung nh\u1ecf $AB$ l\u1ea5y c\u00e1c \u0111i\u1ec3m $M$ v\u00e0 $N$ sao cho $AM = BN$. G\u1ecdi $C$ l\u00e0 giao \u0111i\u1ec3m c\u1ee7a $BN$ v\u00e0 $AM$, $OC$ c\u1eaft $(O)$ t\u1ea1i $E.$ Ch\u1ee9ng minh $\\overset\\frown{AE}=\\overset\\frown{BE}$. ","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],[6],[4],[2]]],"list":[{"point":10,"left":[" $\\Rightarrow \\Delta OAH=\\Delta OBK$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}=\\widehat{{{O}_{4}}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng)","$\\Rightarrow \\widehat{{{O}_{1}}}+\\widehat{{{O}_{2}}}=\\widehat{{{O}_{3}}}+\\widehat{{{O}_{4}}}\\Rightarrow \\widehat{AOC}=\\widehat{BOC}$"," K\u1ebb $OH\\bot AM;OK\\bot BN$ <br\/> V\u00ec $AM=BN\\Rightarrow OH=OK$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y)"," $\\Rightarrow \\text{s\u0111}\\overset\\frown{AE}=\\text{s\u0111}\\overset\\frown{BE}$ hay $ \\overset\\frown{AE}=\\overset\\frown{BE}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 cung) "," Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: $\\Delta OHC=\\Delta OKC$ <br\/> $\\Rightarrow \\widehat{{{O}_{2}}}=\\widehat{{{O}_{3}}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng)"," X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OAH$ v\u00e0 $\\Delta OBK$ c\u00f3: $\\left\\{ \\begin{align} & OA=OB=R \\\\ & OH=OK\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ \\end{align} \\right.$ "],"top":100,"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai14/lv3/img\/h932_K10.png' \/><\/center> <br\/> K\u1ebb $OH\\bot AM;OK\\bot BN$ <br\/> V\u00ec $AM=BN\\Rightarrow OH=OK$ (\u0111\u1ecbnh l\u00ed kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> X\u00e9t hai tam gi\u00e1c vu\u00f4ng $\\Delta OAH$ v\u00e0 $\\Delta OBK$ c\u00f3: <br\/> $\\left\\{ \\begin{align} & OA=OB=R \\\\ & OH=OK\\,\\left( \\text{ch\u1ee9ng minh tr\u00ean} \\right) \\\\ \\end{align} \\right.$ <br\/> $\\Rightarrow \\Delta OAH=\\Delta OBK$ (c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng) <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}=\\widehat{{{O}_{4}}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta \u0111\u01b0\u1ee3c: $\\Delta OHC=\\Delta OKC$ <br\/> $\\Rightarrow \\widehat{{{O}_{2}}}=\\widehat{{{O}_{3}}}$ (hai g\u00f3c t\u01b0\u01a1ng \u1ee9ng) <br\/> $\\Rightarrow \\widehat{{{O}_{1}}}+\\widehat{{{O}_{2}}}=\\widehat{{{O}_{3}}}+\\widehat{{{O}_{4}}}$ <br\/> $\\Rightarrow \\widehat{AOC}=\\widehat{BOC}$ <br\/> $\\Rightarrow \\text{s\u0111}\\overset\\frown{AE}=\\text{s\u0111}\\overset\\frown{BE}$ hay $\\overset\\frown{AE}=\\overset\\frown{BE}$ (\u0111\u1ecbnh l\u00ed li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 cung) <\/span>"}]}],"id_ques":1470}],"lesson":{"save":0,"level":3}}