Bài tập cơ bản bài Liên hệ giữa dây và khoảng cách từ tâm đến dây

Home Lớp 9 Toán lớp 9 Liên hệ giữa dây và khoảng cách từ tâm đến dây Bài tập cơ bản

{"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":60,"content":"","type_input":"","type_check":"","ques":"Cho $PQ$ v\u00e0 $MN$ l\u00e0 hai d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O).$ K\u1ebb $OH \\bot PQ$ t\u1ea1i $H, OK \\bot MN$ t\u1ea1i $K,$ bi\u1ebft r\u1eb1ng $MN = PQ, OK = 2 cm .$ \u0110\u1ed9 d\u00e0i c\u1ea1nh $OH $ l\u00e0 _input_ $(cm)$ <\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D11.jpg' \/><\/center><br\/> Ta c\u00f3: $OH \\bot PQ$ v\u00e0 $OK \\bot MN$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow$ Kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $PQ$ v\u00e0 $MN$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $OH$ v\u00e0 $OK$ <br\/> Do $MN = PQ$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow OH = OK $ (\u0111\u1ecbnh l\u00ed v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> $\\Rightarrow OH= 2\\,(cm)$ <br\/> V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2.$ <\/span> "}]}],"id_ques":1121},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t"]],"list":[{"point":5,"col_name":["","\u0110\u00fang","Sai"],"arr_ques":["Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, hai d\u00e2y b\u1eb1ng nhau th\u00ec c\u00e1ch \u0111\u1ec1u t\u00e2m ","Hai d\u00e2y c\u00e1ch \u0111\u1ec1u t\u00e2m th\u00ec b\u1eb1ng nhau","Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y l\u1edbn h\u01a1n th\u00ec g\u1ea7n t\u00e2m h\u01a1n"],"explain":["\u0110\u00fang, theo \u0111\u1ecbnh l\u00ed v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y <br\/>","Sai, v\u00ec hai d\u00e2y c\u00f3 th\u1ec3 \u1edf hai \u0111\u01b0\u1eddng tr\u00f2n kh\u00e1c nhau <br\/>","\u0110\u00fang, theo \u0111\u1ecbnh l\u00ed v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y"]}]}],"id_ques":1122},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","f","t"]],"list":[{"point":5,"ques":"Cho $AB$ v\u00e0 $CD$ l\u00e0 hai d\u00e2y (kh\u00e1c \u0111\u01b0\u1eddng k\u00ednh) c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; R).$ G\u1ecdi $OH$ v\u00e0 $OK$ theo th\u1ee9 t\u1ef1 l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $AB$ v\u00e0 $CD$","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["N\u1ebfu $AB = CD$ th\u00ec $OH = OK$ ","N\u1ebfu $OH = OK$ th\u00ec $AB = CD$","N\u1ebfu $AB < CD$ th\u00ec $OH < OK$","N\u1ebfu $AB > CD$ th\u00ec $OH < OK$"],"explain":["\u0110\u00fang, v\u00ec trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n hai d\u00e2y b\u1eb1ng nhau th\u00ec c\u00e1ch \u0111\u1ec1u t\u00e2m.","\u0110\u00fang, v\u00ec trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n hai d\u00e2y c\u00e1ch \u0111\u1ec1u t\u00e2m th\u00ec b\u1eb1ng nhau","Sai, v\u00ec n\u1ebfu $AB < CD$ th\u00ec $OH > OK$ ","\u0110\u00fang, v\u00ec trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec g\u1ea7n t\u00e2m h\u01a1n"]}]}],"id_ques":1123},{"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":[[["4"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ c\u00f3 b\u00e1n k\u00ednh $5 cm,$ \u0111\u1ed9 d\u00e0i d\u00e2y $AB = 6 cm.$ V\u1ebd d\u00e2y $CD$ song song v\u1edbi $AB$ c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $8 cm .$ <br\/> C\u00e2u 1: <\/b> Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m $O$ \u0111\u1ebfn $AB $_input_ $(cm)$ <\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D9.jpg' \/><\/center><br\/> K\u1ebb $OH \\bot AB $ <br\/> $\\Rightarrow H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ (\u0111\u1ecbnh l\u00ed quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> $\\Rightarrow AH = HB=\\dfrac{AB}{2}=3\\,(cm)$ <br\/> X\u00e9t $\\Delta AHO$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $AO^2=OH^2+HA^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OH^2= 5^2-3^2 \\\\ \\Rightarrow OH^2= 16 \\\\ \\Rightarrow OH = 4\\,(cm)$ <br\/> Suy ra kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m $O$ \u0111\u1ebfn $AB$ l\u00e0 $ 4\\, cm$ <br\/> V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4.$ <\/span> "}]}],"id_ques":1124},{"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":[[["3"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ c\u00f3 b\u00e1n k\u00ednh $5 cm,$ d\u00e2y $AB = 6 cm.$ V\u1ebd d\u00e2y CD song song v\u1edbi AB c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $8 cm.$ <br\/> C\u00e2u 2: <\/b> Kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $CD =$_input_ $(cm)$ <\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D8.jpg' \/><\/center><br\/> K\u1ebb $OK \\bot CD$ <br\/> $\\Rightarrow K$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $CD$ (\u0111\u1ecbnh l\u00ed quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> $\\Rightarrow CK = KD=\\dfrac{CD}{2}=4\\,(cm)$ <br\/> X\u00e9t $\\Delta DKO$ vu\u00f4ng t\u1ea1i $K$ c\u00f3: <br\/> $DO^2=OK^2+KD^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OK^2= 5^2-4^2\\\\ \\Rightarrow OK^2= 9\\\\ \\Rightarrow OK = 3\\,(cm)$ <br\/> Suy ra kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m $O$ \u0111\u1ebfn $CD$ l\u00e0 $ 3 \\,cm$ <br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $3.$ <\/span> "}]}],"id_ques":1125},{"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":[[["49"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$ c\u00f3 b\u00e1n k\u00ednh $5 cm,$ d\u00e2y $AB = 6 cm.$ V\u1ebd d\u00e2y $CD$ song song v\u1edbi $AB$ c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $8 cm$ <br\/> C\u00e2u 3: <\/b> Di\u1ec7n t\u00edch h\u00ecnh thang $ABCD$ l\u00e0 _input_$cm^2$<\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_8.jpg' \/><\/center><br\/>V\u00ec $AB \/\/ CD,$ $OH \\bot AB,$ $OK \\bot CD$ <br\/>Suy ra ba \u0111i\u1ec3m $O, H, K$ th\u1eb3ng h\u00e0ng <br\/> $\\Rightarrow HK = OH + HK $ $=4+3= 7\\,(cm)$ <br\/> Di\u1ec7n t\u00edch h\u00ecnh thang $ABCD $ l\u00e0: <br\/> $S = \\dfrac{(AB+CD).HK}{2}$ $=\\dfrac{(6+8).7}{2}=49\\,(cm^2)$ <br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $49.$ <\/span> <\/span>"}]}],"id_ques":1126},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"select":["A. $\\sqrt{2}$","B. $2\\sqrt{2}$","C. $3\\sqrt{2}$"],"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$, b\u00e1n k\u00ednh $3 cm$ v\u00e0 d\u00e2y cung $AB =2 cm.$ <br\/>Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m $O$ \u0111\u1ebfn $AB$ l\u00e0 ?$(cm)$","hint":"K\u1ebb $OH \\bot AB$ ","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D5.jpg' \/><\/center><br\/> K\u1ebb $OH \\bot AB$ t\u1ea1i $H$ <br\/> $\\Rightarrow H$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ (\u0111\u1ecbnh l\u00ed quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> $\\Rightarrow AH = HB =\\dfrac{AB}{2}=1\\,(cm)$ <br\/> X\u00e9t $\\Delta AOH$ vu\u00f4ng t\u1ea1i $H$ c\u00f3: <br\/> $OA^2=OH^2+AH^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OH^2= 3^2-1^2\\\\ \\Rightarrow OH^2=8\\\\ \\Rightarrow OH =2\\sqrt{2}\\,(cm)$"}]}],"id_ques":1127},{"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 \u0111\u01b0\u1eddng tr\u00f2n $(O),$ hai d\u00e2y $PQ, RS.$ H\u1ea1 $OH \\bot PQ,$ $OK \\bot RS.$ <br\/> Ta c\u00f3 $OH = OK \\Leftrightarrow PQ $ _input_$RS$","explain":"Theo \u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y th\u00ec $OH = OK \\Leftrightarrow PQ = RS$ <br\/> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u =<\/span>"}]}],"id_ques":1128},{"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 ch\u1ed7 tr\u1ed1ng","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, hai d\u00e2y . . . th\u00ec c\u00e1ch \u0111\u1ec1u ...","select":["A. B\u1eb1ng nhau, t\u00e2m","B. C\u1eaft nhau, t\u00e2m","C. Vu\u00f4ng g\u00f3c, t\u00e2m"],"explain":" Trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, hai d\u00e2y b\u1eb1ng nhau th\u00ec c\u00e1ch \u0111\u1ec1u t\u00e2m <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":3}]}],"id_ques":1129},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["f","t","t","t"]],"list":[{"point":5,"ques":"Cho $EF$ v\u00e0 $IK$ l\u00e0 hai d\u00e2y (kh\u00e1c \u0111\u01b0\u1eddng k\u00ednh) c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n $(O; R).$ G\u1ecdi $OA$ v\u00e0 $OB$ theo th\u1ee9 t\u1ef1 l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $EF$ v\u00e0 $IK$","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["N\u1ebfu $EF > IK$ th\u00ec $OA > OB$ ","N\u1ebfu $EF = IK$ th\u00ec $OA = OB$","N\u1ebfu $EF < IK$ th\u00ec $OA > OB$","N\u1ebfu $OA = OB$ th\u00ec $EF = IK$ "],"explain":["Sai, v\u00ec d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec g\u1ea7n t\u00e2m h\u01a1n <br\/> $\\Rightarrow$ N\u1ebfu $EF > IK$ th\u00ec $OA < OB$ <br\/>","\u0110\u00fang, do trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n hai d\u00e2y b\u1eb1ng nhau th\u00ec c\u00e1ch \u0111\u1ec1u t\u00e2m<br\/>","\u0110\u00fang, do trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec g\u1ea7n t\u00e2m h\u01a1n <br\/>","\u0110\u00fang, do trong m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n hai d\u00e2y c\u00e1ch \u0111\u1ec1u t\u00e2m th\u00ec b\u1eb1ng nhau"]}]}],"id_ques":1130},{"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 tam gi\u00e1c $ABC$ c\u00e2n t\u1ea1i $A$ v\u00e0 n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O).$ G\u1ecdi $OP, OE, OF$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $AB, AC, BC.$ Ta c\u00f3 ","select":["A. $OP = OE = OF$","B. $OP = OE$","C. $OE = OF$","D. $OE = OF$"],"explain":"<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/h922_1.png' \/><\/center> $\\Delta ABC$ c\u00e2n t\u1ea1i $A$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow AB = AC$ (t\u00ednh ch\u1ea5t tam gi\u00e1c c\u00e2n) <br\/> Suy ra $OP = OE$ (\u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> T\u01b0\u01a1ng t\u1ef1: Do $BC \\ne AB$ v\u00e0 $BC \\ne AC$ n\u00ean c\u00e1c m\u1ec7nh \u0111\u1ec1 $OE = OF$ v\u00e0 $OP = OF$ l\u00e0 sai <br\/> $\\Rightarrow OP = OE = OF$ c\u0169ng l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 kh\u00f4ng \u0111\u00fang<br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":1131},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u > , < , = th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho h\u00ecnh 1 trong \u0111\u00f3 hai \u0111\u01b0\u1eddng trong c\u00f9ng c\u00f3 t\u00e2m $O$. Cho bi\u1ebft $AB > AC.$ <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D2.jpg' \/><\/center> <br\/> C\u00e2u 1:<\/b> So s\u00e1nh $OH$ v\u00e0 $OK$ <br\/> \u0110\u00e1p s\u1ed1: <\/b> $OH$ _input_ $OK$","hint":"Trong hai d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec d\u00e2y \u0111\u00f3 g\u1ea7n t\u00e2m h\u01a1n","explain":" X\u00e9t \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn, Theo \u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y <br\/> $AB > AC \\Rightarrow OH < OK$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u < <\/span> "}]}],"id_ques":1132},{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u > , < , = th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":" Cho h\u00ecnh 1 trong \u0111\u00f3 hai \u0111\u01b0\u1eddng trong c\u00f9ng c\u00f3 t\u00e2m $O$. <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D2.jpg' \/><\/center> <br\/> C\u00e2u 2:<\/b> Cho bi\u1ebft $AB > AC.$ H\u00e3y so s\u00e1nh $HM$ v\u00e0 $DK$ <br\/> \u0110\u00e1p s\u1ed1: <\/b> $HM$ _input_ $DK$","explain":"X\u00e9t \u0111\u01b0\u1eddng tr\u00f2n nh\u1ecf, ta c\u00f3: $OH < OK$ (theo c\u00e2u 1) (1)<br\/> $\\Rightarrow EM > DF$ (\u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/> M\u00e0 $OH \\bot EM$ <br\/> $\\Rightarrow HE=HM=\\dfrac{EM}{2}$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) (2) <br\/> $OK \\bot DF$ <br\/> $\\Rightarrow FK= KD=\\dfrac{DF}{2}$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) (3) <br\/> T\u1eeb (1), (2), (3) suy ra $HM > DK$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u > <\/span><\/span> "}]}],"id_ques":1133},{"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 \u0111\u01b0\u1eddng tr\u00f2n $(O),$ hai d\u00e2y $PQ, RS.$ H\u1ea1 $OH \\bot PQ,$ $OK \\bot RS.$ <br\/>Ta c\u00f3 $OH < OK$ $\\Leftrightarrow PQ$ _input_$RS$ ","explain":"Theo \u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y <br\/> $ OH < OK \\Leftrightarrow PQ > RS$ <br\/>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u > <\/span>"}]}],"id_ques":1134},{"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 tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O).$ G\u1ecdi $OM, ON, OP$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn $BC, AC, AB$ v\u00e0 c\u00f3 $OM < ON < OP.$ So s\u00e1nh $AB, AC, BC$","select":["A. $ AC > AB > BC $","B. $ AB < BC < AC $","C. $ BC > AC > AB $","D. $ BC < AC < AB $"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D1.1.jpg' \/><\/center> Ta c\u00f3: $OM < ON < OP $ (gi\u1ea3 thi\u1ebft) <br\/> $ \\Rightarrow BC > AC > AB$ (\u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y) <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":1135},{"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 ch\u1ed7 tr\u1ed1ng","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Trong hai d\u00e2y c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec . . .","select":["A. C\u00e1ch \u0111\u1ec1u t\u00e2m","B. D\u00e2y \u0111\u00f3 g\u1ea7n t\u00e2m h\u01a1n","C. D\u00e2y \u0111\u00f3 xa t\u00e2m h\u01a1n"],"explain":" Trong hai d\u00e2y c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, d\u00e2y n\u00e0o l\u1edbn h\u01a1n th\u00ec g\u1ea7n t\u00e2m h\u01a1n <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B<\/span>","column":3}]}],"id_ques":1136},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n $(O; 1,5 cm)$ v\u00e0 d\u00e2y $AB$ di \u0111\u1ed9ng sao cho $AB = 2,4 cm.$ Khi \u0111\u00f3, trung \u0111i\u1ec3m $M$ c\u1ee7a $AB$ di \u0111\u1ed9ng tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; 0,81 cm)$","select":["A. \u0110\u00fang","B. Sai"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pitago \u0111\u1ec3 t\u00ednh $OM$","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D4.jpg' \/><\/center><br\/> Ta c\u00f3: $M$ l\u00e0 trung \u0111i\u1ec3m c\u1ee7a $AB$ <br\/> $\\Rightarrow AM = MB= \\dfrac{AB}{2} = 1,2 \\, (cm)$ <br\/> $\\Rightarrow OM \\bot AB$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y cung) <br\/> X\u00e9t $\\Delta AOM$ vu\u00f4ng t\u1ea1i $M$ c\u00f3: <br\/> $OA^2=OM^2+AM^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OM^2=1,5^2 - 1,2^2 \\\\ \\Rightarrow OM^2=0,81\\\\ \\Rightarrow OM =0,9\\, (cm) $<br\/> Suy ra trung \u0111i\u1ec3m $M$ c\u1ee7a $AB$ di \u0111\u1ed9ng tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n $(O; 0,9 cm)$ <br\/>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai <br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span> ","column":2}]}],"id_ques":1137},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","f"]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n $(O)$ c\u00f3 $\\widehat{A}<\\widehat{B}<\\widehat{C}<90^o$. G\u1ecdi $M, N, P$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh $BC, CA, AB.$ Khi \u0111\u00f3","col_name":["","\u0110\u00fang","Sai"],"arr_ques":["$cos \\widehat{A} > cos \\widehat{B} > cos \\widehat{C} $","$BC < AC < AB$","$OM < ON < OP$"],"explain":["\u0110\u00fang, v\u00ec trong c\u00e1c g\u00f3c nh\u1ecdn, g\u00f3c n\u00e0o nh\u1ecf h\u01a1n th\u00ec gi\u00e1 tr\u1ecb c\u00f4sin c\u1ee7a n\u00f3 l\u1edbn h\u01a1n","\u0110\u00fang v\u00ec $\\widehat{A}<\\widehat{B}<\\widehat{C}$ (gi\u1ea3 thi\u1ebft) <br\/> $\\Rightarrow BC < AC < AB$ (quan h\u1ec7 gi\u1eefa g\u00f3c v\u00e0 c\u1ea1nh \u0111\u1ed1i di\u1ec7n trong m\u1ed9t tam gi\u00e1c)"," Sai, Ta c\u00f3 $OM \\bot BC,$ $ON \\bot CA,$ $OP \\bot AB.$ <br\/> $\\Rightarrow$ kho\u1ea3ng c\u00e1ch t\u1eeb c\u00e1c c\u1ea1nh $BC, CA, AB$ \u0111\u1ebfn t\u00e2m l\u1ea7n l\u01b0\u1ee3t l\u00e0 $OM, ON, OP$ <br\/> Do $ BC < AC < AB$ (ch\u1ee9ng minh tr\u00ean) <br\/> Suy ra $OM > ON > OP$ (\u0111\u1ecbnh l\u00ed v\u1ec1 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y)"]}]}],"id_ques":1138},{"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":[[["3"],["7"]]],"list":[{"point":5,"width":60,"content":"","type_input":"","type_check":"","ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$, hai d\u00e2y $AB$ v\u00e0 $CD$ vu\u00f4ng g\u00f3c v\u1edbi nhau \u1edf $M.$ Bi\u1ebft $AB = 20 cm ,$ $CD = 16 cm,$ $MA = 3 cm$ v\u00e0 $MC = 5 cm.$ <br\/> C\u00e2u 1:<\/b> T\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn m\u1ed7i d\u00e2y.<br\/> \u0110\u00e1p s\u1ed1: <\/b> Kho\u1ea3ng c\u00e1ch t\u1eeb $O$ \u0111\u1ebfn c\u00e1c d\u00e2y $AB$ v\u00e0 $CD$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 _input_ $(cm)$ v\u00e0 _input_ $(cm)$ <\/span>","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D3.jpg' \/><\/center><br\/> K\u1ebb $OH \\bot CD$ <br\/> $\\Rightarrow HC= HD=\\dfrac{CD}{2}=8\\,(cm)$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> K\u1ebb $OK \\bot AB$ <br\/> $\\Rightarrow KA= KB=\\dfrac{AB}{2}=10\\,(cm)$ (quan h\u1ec7 vu\u00f4ng g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y) <br\/> $MH = HC - MC = 8 - 5 = 3\\, (cm)$ <br\/> $MK = KA - MA = 10 - 3 = 7\\, (cm)$ <br\/> T\u1ee9 gi\u00e1c $OHMK$ l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt ($\\widehat{M}=\\widehat{H}=\\widehat{K}={{90}^{o}}$) <br\/> Suy ra $OH = MK = 7\\, cm,$ $OK = MH = 3\\, cm$ <br\/> V\u1eady kho\u1ea3ng c\u00e1c t\u1eeb $O$ \u0111\u1ebfn c\u00e1c d\u00e2y $AB$ v\u00e0 $CD$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $3 cm$ v\u00e0 $7 cm$ <br\/>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $3$ v\u00e0 $7.$<\/span> <\/span>"}]}],"id_ques":1139},{"time":24,"part":[{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m $O$, hai d\u00e2y $AB$ v\u00e0 $CD$ vu\u00f4ng g\u00f3c v\u1edbi nhau \u1edf $M.$ Bi\u1ebft $AB = 20 cm ,$ $CD = 16 cm,$ $MA = 3 cm$ v\u00e0 $MC = 5 cm.$ <br\/> C\u00e2u 2:<\/b> B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n $(O)$ l\u00e0:<\/span>","select":["A. $\\sqrt{149}\\, cm$","B. $\\sqrt{91}\\, cm$","C. $3\\sqrt{11}\\, cm$","D. $\\sqrt{109}\\, cm$"],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pitago \u0111\u1ec3 t\u00ednh c\u1ea1nh $AO$","explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai7/lv1/img\/H922_D3.jpg' \/><\/center><br\/> X\u00e9t $\\Delta AOK$ vu\u00f4ng t\u1ea1i $K$ c\u00f3: <br\/> $OA^2=AK^2+OK^2$ (\u0111\u1ecbnh l\u00ed Pitago) <br\/> $\\Rightarrow OA^2=10^2+3^2\\\\ \\Rightarrow OA^2= 100 + 9 = 109\\\\ \\Rightarrow OA= \\sqrt{109}\\,(cm)$<br\/>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span> ","column":4}]}],"id_ques":1140}],"lesson":{"save":0,"level":1}}

Điểm của bạn.

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)

Điểm của bạn.

Bấm vào đây nếu phát hiện có lỗi hoặc muốn gửi góp ý

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