Sự đồng quy của ba đường trung tuyến, ba đường phân giác trong một tam giác

Home Toán lớp 7 - tập 2 Chương 9: Quan hệ giữa các yếu tố trong một tam giác Bài 34: Sự đồng quy của ba đường trung tuyến, ba đường phân giác trong một tam giácBài tập nâng cao

{"common":{"save":0,"post_id":"5841","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8729","post_id":"5841","mon_id":"1158532","chapter_id":"1158662","question":"Cho tam giác ABC v\u1edbi hai \u0111\u01b0\u1eddng trung tuy\u1ebfn AM và BN và tr\u1ecdng tâm G c\u1ee7a tam giác ABC.<\/p>Ch\u1ecdn các s\u1ed1 thích h\u1ee3p \u0111\u1eb7t vào ch\u1ed7 tr\u1ed1ng \u0111\u1ec3 \u0111\u01b0\u1ee3c \u0111\u1eb3ng th\u1ee9c:<\/p>$\\dfrac{BG}{BN}=$<\/span> <input class=\"_tit_hoi\" disabled=\"disabled\" type=\"text\"\/> ; $\\dfrac{GN}{GB}=$<\/span> <input class=\"_tit_hoi\" disabled=\"disabled\" type=\"text\"\/><\/p>","options":["A.<\/strong> $\\dfrac{3}{2}$<\/span> ; $\\dfrac{1}{2}$<\/span>","B.<\/strong> $\\dfrac{2}{3}$<\/span> ; $\\dfrac{1}{3}$<\/span>","C.<\/strong> $\\dfrac{2}{3}$<\/span> ; $2$<\/span>","D.<\/strong> $\\dfrac{2}{3}$<\/span> ; $\\dfrac{1}{2}$<\/span>"],"correct":"4","level":"3","hint":"Tr\u1ecdng tâm tam giác cách m\u1ed7i \u0111\u1ec9nh c\u1ee7a tam giác m\u1ed9t kho\u1ea3ng b\u1eb1ng $\\dfrac{2}{3}$<\/span> \u0111\u1ed9 dài \u0111\u01b0\u1eddng trung tuy\u1ebfn \u0111i qua \u0111\u1ec9nh \u1ea5y.  <\/p>","answer":"Ta có hình v\u1ebd:<\/p><svg height=\"170\" width=\"270\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"272\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_19\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_9\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"21.0125\" x2=\"246.0125\" y1=\"131.2375\" y2=\"131\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"90.0125\" x2=\"21.0125\" y1=\"19.2375\" y2=\"131.2375\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"244.0125\" x2=\"90.01249\" y1=\"130.2375\" y2=\"21.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"88.0125\" x2=\"136.01251\" y1=\"20.2375\" y2=\"131.2375\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"61.0125\" xml:space=\"preserve\" y=\"25.2375\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"126.0125\" xml:space=\"preserve\" y=\"156.2375\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"7.0125\" xml:space=\"preserve\" y=\"156.2375\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"237.0125\" xml:space=\"preserve\" y=\"153.2375\">C<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"77.0125\" x2=\"82.0125\" y1=\"124.2375\" y2=\"138.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"171.0125\" x2=\"178.0125\" y1=\"121.2375\" y2=\"136.2375\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"90.0125\" xml:space=\"preserve\" y=\"91.2375\">G<\/text> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"22.0125\" x2=\"165.01251\" y1=\"130.2375\" y2=\"74.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"126.0125\" x2=\"139.0125\" y1=\"53.2375\" y2=\"46.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"129.0125\" x2=\"142.0125\" y1=\"57.2375\" y2=\"50.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_16\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"175.0125\" x2=\"190.0125\" y1=\"93.2375\" y2=\"83.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_17\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"180.0125\" x2=\"195.0125\" y1=\"95.2375\" y2=\"85.2375\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"167.0125\" xml:space=\"preserve\" y=\"71.2375\">N<\/text> <\/g> <\/svg><\/span><\/p>\u0110\u1eb7t  $BN = x\u00a0\\space\\space (x > 0)$<\/span><\/p>Vì G là tr\u1ecdng tâm tam giác ABC nên $BG=\\dfrac{2}{3}.BN=\\dfrac{2}{3}x$<\/span><\/p>M\u1eb7t khác $BG + GN = BN$<\/span><\/p>nên          $\\dfrac{2}{3}x+GN=x$<\/span><\/p>suy ra                $GN=x-\\dfrac{2}{3}x=\\dfrac{1}{3}x$<\/span><\/p>Ta có: $\\dfrac{BG}{BN}=\\dfrac{\\dfrac{2}{3}.x}{x}=\\dfrac{2}{3}$<\/span>    ;  $\\dfrac{GN}{GB}=\\dfrac{\\dfrac{1}{3}.x}{\\dfrac{2}{3}.x}=\\dfrac{1}{2}$<\/span><\/p>V\u1eady $\\dfrac{BG}{BN}=\\dfrac{2}{3}$<\/span> ;  $\\dfrac{GN}{GB}=\\dfrac{1}{2}$<\/span><\/p>\u0110áp án \u0111úng là D.<\/strong>  $\\dfrac{2}{3}$<\/span> ; $\\dfrac{1}{2}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-04 10:41:53","option_type":"math","len":0},{"id":"8733","post_id":"5841","mon_id":"1158532","chapter_id":"1158662","question":"Cho tam giác ABD, có BO và DO là các \u0111\u01b0\u1eddng phân giác. Bi\u1ebft $\\widehat{D_1}=30^0$<\/span> ; $\\widehat{B_2}=20^0$<\/span>. Tính s\u1ed1 \u0111o các góc $\\widehat{A_1}$<\/span> ; $\\widehat{O_1}$<\/span><\/p><svg height=\"170\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_29\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><path fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <path fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <path fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <g id=\"svg_17\"> <g id=\"svg_4\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"7.30625\" x2=\"219.30625\" y1=\"139.2375\" y2=\"139\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" transform=\"rotate(60 184.15312194824213,79.11875915527345) \" x1=\"114\" x2=\"254.30625\" y1=\"79.2375\" y2=\"79\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(-40 78.49999999999997,79.11874389648438) \" x1=\"-13\" x2=\"170\" y1=\"79.2375\" y2=\"79\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(10 143.30625915527352,55.618751525878984) \" x1=\"143.30625\" x2=\"143.30625\" y1=\"20.2375\" y2=\"91\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(70 74.30625152587889,115.11874389648439) \" x1=\"74.30625\" x2=\"74.30625\" y1=\"47.2375\" y2=\"183\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"137.30625\" x2=\"219.30625\" y1=\"92.2375\" y2=\"139.2375\"><\/line> <path d=\"m45.30625,106.2375c0,0 13,3 7,16\" fill=\"none\" fill-opacity=\"null\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <path d=\"m53.30625,123.2375c0,0 13,3 7,16\" fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <path d=\"m181.30625,118.2375c-18,6 -4,20 -4,20\" fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <path d=\"m193.30625,99.2375c-18,6 -4,20 -4,20\" fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(40.644432067871094 188.71267700195315,109.23750305175778) \"><\/path> <path d=\"m195.54749,103.88886c-15.02676,5.60918 -3.33928,18.69727 -3.33928,18.69727\" fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(40.644432067871094 191.7126770019531,113.23749542236331) \"><\/path> <path d=\"m185.30625,120.2375c-14.08148,5.7 -3.12922,19 -3.12922,19\" fill=\"none\" fill-opacity=\"null\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/path> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"108.30625\" xml:space=\"preserve\" y=\"23.2375\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.30625\" xml:space=\"preserve\" y=\"166.2375\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"209.30625\" xml:space=\"preserve\" y=\"166.2375\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"125.30625\" xml:space=\"preserve\" y=\"121.2375\">O<\/text> <text fill=\"#ff0000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_22\" stroke=\"#ff0000\" stroke-width=\"0\" text-anchor=\"start\" x=\"146.30625\" xml:space=\"preserve\" y=\"45.2375\">1<\/text> <text fill=\"#ff0000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"141.30625\" xml:space=\"preserve\" y=\"92.2375\">1<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"193.30625\" xml:space=\"preserve\" y=\"124.2375\">1<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_25\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.30625\" xml:space=\"preserve\" y=\"122.2375\">1<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_26\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"47.30625\" xml:space=\"preserve\" y=\"138.2375\">2<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_27\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.30625\" xml:space=\"preserve\" y=\"137.2375\">2<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\widehat{A_1}=80^0$<\/span> ; $\\widehat{O_1}=110^0$<\/span>","B.<\/strong> $\\widehat{A_1}=40^0$<\/span> ; $\\widehat{O_1}=110^0$<\/span>","C.<\/strong> $\\widehat{A_1}=40^0$<\/span> ; $\\widehat{O_1}=100^0$<\/span>","D.<\/strong> $\\widehat{A_1}=50^0$<\/span> ; $\\widehat{O_1}=110^0$<\/span>"],"correct":"2","level":"3","hint":"Ba \u0111\u01b0\u1eddng phân giác c\u1ee7a m\u1ed9t tam giác \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m. <\/p>N\u1ebfu Ot là tia phân giác c\u1ee7a góc xOy thì $\\widehat{xOt}=\\widehat{tOy}=\\dfrac{1}{2}\\widehat{xOy}$<\/span>.<\/p>T\u1ed5ng ba góc trong m\u1ed9t tam giác b\u1eb1ng 180°.<\/p>","answer":"Vì BO là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc ABD nên $\\widehat{ABD}=2.\\widehat{B_2}=2\\space.\\space20^0=40^0$<\/span><\/p>Vì DO là \u0111\u01b0\u1eddng phân giác c\u1ee7a góc ADB nên $\\widehat{ADB}=2.\\widehat{D_1}=2\\space.\\space30^0=60^0$<\/span><\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí t\u1ed5ng ba góc trong tam giác ABD, ta có:<\/p>$\\widehat{BAD}$<\/span> <\/span>$+\\widehat{ABD}+\\widehat{ADB}=180^0$<\/span><\/p>$\\widehat{BAD}$<\/span><\/span> $+40^0+60^0=180^0$<\/span>. Suy ra $\\widehat{BAD}=80^0$<\/span><\/span><\/p>Vì BO và DO là các \u0111\u01b0\u1eddng phân giác nên AO là \u0111\u01b0\u1eddng phân giác c\u1ee7a $\\widehat{BAD}$<\/span><\/p>Suy ra $\\widehat{A_1}=\\dfrac{1}{2}.\\widehat{BAD}=\\dfrac{1}{2}.80^0=40^0$<\/span><\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí t\u1ed5ng ba góc trong tam giác AOD, ta có:<\/p>$\\widehat{O_1}+\\widehat{A_1}+\\widehat{D_1}=180^0$<\/span><\/p>$\\widehat{O_1}+40^0+30^0=180^0$<\/span>. Suy ra $\\widehat{O_1}=110^0$<\/span><\/p>V\u1eady \u0111áp án \u0111úng là  B.<\/strong> $\\widehat{A_1}=40^0$<\/span> ; $\\widehat{O_1}=110^0$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"1","date":"2022-06-05 03:38:53","option_type":"math","len":0},{"id":"8736","post_id":"5841","mon_id":"1158532","chapter_id":"1158662","question":"Cho hình v\u1ebd.  G là tr\u1ecdng tâm c\u1ee7a tam giác ABC. Tính \u0111\u1ed9 dài x , y trên hình v\u1ebd.<\/p><svg height=\"210\" width=\"350\"> <g><title><\/title><rect fill=\"#ffffff\" height=\"212\" id=\"canvas_background\" width=\"352\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_7\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_9\" stroke=\"null\"> <g id=\"svg_4\" stroke=\"null\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"16.28286\" x2=\"343.30627\" y1=\"175.86031\" y2=\"175.53323\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"127.92429\" x2=\"15.30625\" y1=\"24.36908\" y2=\"177.2375\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"343.30627\" x2=\"127.92429\" y1=\"175.86031\" y2=\"21.61469\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"127.92429\" x2=\"182.82558\" y1=\"20.2375\" y2=\"174.48312\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"16.71398\" x2=\"240.54232\" y1=\"174.48312\" y2=\"100.1147\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"343.30627\" x2=\"70.20754\" y1=\"174.48312\" y2=\"98.7375\"><\/line> <\/g> <text fill=\"#0000ff\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(72.51741790771484 157.1917877197266,77.23749542236327) \" x=\"145.30625\" xml:space=\"preserve\" y=\"83.2375\">4,2<\/text> <text fill=\"#0000ff\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(71.66221618652344 186.11875915527347,154.23751831054688) \" x=\"174.30625\" xml:space=\"preserve\" y=\"160.2375\">2,1<\/text> <text fill=\"#0000ff\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(18.906383514404297 116.11875152587876,102.2374954223633) \" x=\"104.30625\" xml:space=\"preserve\" y=\"108.2375\">3,1<\/text> <text fill=\"#0000ff\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-18.267024993896484 95.19177246093751,139.23750305175784) \" x=\"83.30625\" xml:space=\"preserve\" y=\"145.2375\">5,2<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"9.30625\" xml:space=\"preserve\" y=\"201.2375\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"100.30625\" xml:space=\"preserve\" y=\"21.2375\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"324.30625\" xml:space=\"preserve\" y=\"202.2375\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"248.30625\" xml:space=\"preserve\" y=\"99.2375\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"177.30625\" xml:space=\"preserve\" y=\"203.2375\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"46.30625\" xml:space=\"preserve\" y=\"101.2375\">E<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"147.30625\" xml:space=\"preserve\" y=\"150.2375\">G<\/text> <text fill=\"#ff0000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"191.30625\" xml:space=\"preserve\" y=\"111.2375\">x<\/text> <text fill=\"#ff0000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"243.30625\" xml:space=\"preserve\" y=\"142.2375\">y<\/text> <line fill=\"none\" id=\"svg_14\" stroke=\"#ff0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.9\" x1=\"164.30625\" x2=\"239.30625\" y1=\"126.2375\" y2=\"100.2375\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_24\" stroke=\"#ff0000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.9\" x1=\"163.30625\" x2=\"340.30625\" y1=\"124.2375\" y2=\"174.2375\"><\/line> <line fill=\"none\" id=\"svg_25\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"111.30625\" x2=\"116.30625\" y1=\"166.2375\" y2=\"183.2375\"><\/line> <line fill=\"none\" id=\"svg_26\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"237.30625\" x2=\"243.30625\" y1=\"165.2375\" y2=\"183.2375\"><\/line> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> x = 7,8 ; y = 6,2","B.<\/strong> x = 2,6 ; y = 9,3","C.<\/strong> x = 2,6 ; y = 6,2","D.<\/strong> x = 6,2 ; y = 2,6"],"correct":"3","level":"3","hint":"Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a m\u1ed9t tam giác cùng \u0111i qua 1 \u0111i\u1ec3m. \u0110i\u1ec3m \u0111ó cách m\u1ed7i \u0111\u1ec9nh c\u1ee7a tam giác m\u1ed9t kho\u1ea3ng b\u1eb1ng $\\dfrac{2}{3}$<\/span> \u0111\u1ed9 dài \u0111\u01b0\u1eddng trung tuy\u1ebfn \u0111i qua \u0111\u1ec9nh \u1ea5y.<\/p>","answer":"Vì AN=CN nên N là trung \u0111i\u1ec3m c\u1ee7a AC. Suy ra BN là \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/p>Ta có: BN = BG + GN = 4,2 + 2,1 = 6,3<\/p>Suy ra $\\dfrac{BG}{BN}=\\dfrac{4,2}{6,3}=\\dfrac{2}{3}$<\/span> hay $BG=\\dfrac{2}{3}BN$<\/span>.<\/p>Do \u0111ó G là tr\u1ecdng tâm tam giác ABC.<\/p>T\u1eeb hình v\u1ebd ta có AM , BN , CE \u0111\u1ed3ng quy t\u1ea1i G nên AM và CE c\u0169ng là các \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/p>Ta có: x = GM = $\\dfrac{1}{2}AG=\\dfrac{1}{2}.5,2=2,6$<\/span><\/p>y = CG = 2 . GE = 2 . 3,1 = 6,2<\/p>V\u1eady \u0111áp án \u0111úng là C.<\/strong> x = 2,6 ; y = 6,2<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"131","test":"3","date":"2022-06-05 04:19:06","option_type":"txt","len":2}]}