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{"common":{"save":0,"post_id":"7301","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7525","mon_id":"1158767","chapter_id":"1159256","post_id":"7301","question":"<p>Cho tam gi&aacute;c ABC c&oacute; tr\u1ecdng t&acirc;m G v&agrave; M l&agrave; \u0111i\u1ec3m t&ugrave;y &yacute;. Kh\u1eb3ng \u0111\u1ecbnh n&agrave;o sau \u0111&acirc;y <strong>sai<\/strong>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{AM}+\\overrightarrow{BM}+\\overrightarrow{CM}=3\\overrightarrow{GM}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=3\\overrightarrow{GM}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{MA}+\\overrightarrow{MB}+\\overrightarrow{MC}=3\\overrightarrow{MG}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=\\overrightarrow{0}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>V&igrave; G l&agrave; tr\u1ecdng t&acirc;m c\u1ee7a tam gi&aacute;c ABC v&agrave; M l&agrave; \u0111i\u1ec3m t&ugrave;y &yacute;&nbsp;n&ecirc;n<\/p><p><span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=\\overrightarrow{0}$<\/span>&nbsp; (<strong>D<\/strong> \u0111&uacute;ng, <span style=\"color:#16a085;\"><strong>B<\/strong> sai<\/span>)<\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MA}-\\overrightarrow{MG}+\\overrightarrow{MB}-\\overrightarrow{MG}+\\overrightarrow{MC}-\\overrightarrow{MG}=\\overrightarrow{0}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MA}+\\overrightarrow{MB}+\\overrightarrow{MC}=3\\overrightarrow{MG}$<\/span>&nbsp; (<strong>C<\/strong>&nbsp;\u0111&uacute;ng)<\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AM}+\\overrightarrow{BM}+\\overrightarrow{MC}=3\\overrightarrow{GM}$<\/span>&nbsp; (<strong>A<\/strong>&nbsp;\u0111&uacute;ng)<\/p><p>C&acirc;u <strong>sai <\/strong>l&agrave;&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=3\\overrightarrow{GM}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 04:55:24","option_type":"math","len":0},{"id":"7528","mon_id":"1158767","chapter_id":"1159256","post_id":"7301","question":"<p>Cho h&igrave;nh b&igrave;nh h&agrave;nh ABCD c&oacute; t&acirc;m I. Khi \u0111&oacute; vect\u01a1 t\u1ed5ng&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}+\\overrightarrow{AC}+\\overrightarrow{AD}$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$2\\overrightarrow{AI}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$4\\overrightarrow{IA}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$4\\overrightarrow{AI}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$2\\overrightarrow{IA}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p><span class=\"svgedit\"><svg height=\"180\" width=\"340\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"182\" id=\"canvas_background\" width=\"342\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g>&lt;title&gt;&lt;\/title><g id=\"svg_13\"> <g id=\"svg_6\"> <g id=\"svg_4\"> <path d=\"m21.0925,159.35209l59.4,-131l237.59999,0l-59.4,131l-237.59999,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"79.5\" x2=\"259.5\" y1=\"28.25\" y2=\"160.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"22.5\" x2=\"318.5\" y1=\"159.25\" y2=\"28.25\"><\/line> <\/g> <ellipse cx=\"217\" cy=\"72.75\" fill=\"#bf0000\" id=\"svg_5\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <\/g> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.5\" xml:space=\"preserve\" y=\"165.25\">A<\/text> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"63.5\" xml:space=\"preserve\" y=\"27.25\">B<\/text> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"319.5\" xml:space=\"preserve\" y=\"27.25\">C<\/text> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"264.5\" xml:space=\"preserve\" y=\"164.25\">D<\/text> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"162.5\" xml:space=\"preserve\" y=\"113.25\">I<\/text> <text fill=\"#000000\" font-family=\"&rsquo;Times New Roman&rsquo;, Times, serif\" font-size=\"20\" font-weight=\"bold\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"207.5\" xml:space=\"preserve\" y=\"62.25\">G<\/text> <\/g> <\/g> <\/svg><\/span><\/p><p>G\u1ecdi G l&agrave; tr\u1ecdng t&acirc;m tam gi&aacute;c BCD.<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}+\\overrightarrow{AC}+\\overrightarrow{AD}=3\\overrightarrow{AG}=3.\\dfrac{4}{3}.\\overrightarrow{AI}=4\\overrightarrow{AI}$<\/span>&nbsp;.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$4\\overrightarrow{AI}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 05:04:06","option_type":"math","len":0},{"id":"7531","mon_id":"1158767","chapter_id":"1159256","post_id":"7301","question":"<p>G\u1ecdi G l&agrave; tr\u1ecdng t&acirc;m c\u1ee7a tam gi&aacute;c ABC. \u0110\u1eb7t&nbsp;<span class=\"math-tex\">$\\overrightarrow{a}=\\overrightarrow{GA};\\overrightarrow{b}=\\overrightarrow{GC}$<\/span>. \u0110\u1eb3ng th\u1ee9c n&agrave;o d\u01b0\u1edbi \u0111&acirc;y l&agrave; \u0111&uacute;ng?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{CA}=-2\\overrightarrow{a}-\\overrightarrow{b}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{CA}=2\\overrightarrow{a}+\\overrightarrow{b}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{CA}=\\dfrac{4}{3}\\overrightarrow{a}+\\dfrac{1}{3}\\overrightarrow{b}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{CA}=\\dfrac{2}{3}\\overrightarrow{a}-\\dfrac{1}{3}\\overrightarrow{b}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p><span class=\"svgedit\"><svg height=\"240\" width=\"350\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"242\" id=\"canvas_background\" width=\"352\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g>&lt;title&gt;&lt;\/title><image height=\"227\" id=\"svg_2\" width=\"347\" x=\"1.5\" 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\" y=\"-0.5\"><\/image> <\/g> <\/svg><\/span><\/p><p>G\u1ecdi D, E, F l\u1ea7n l\u01b0\u1ee3t l&agrave; trung \u0111i\u1ec3m c\u1ee7a AB, AC, BC.<\/p><p>V&igrave; G l&agrave; tr\u1ecdng t&acirc;m c\u1ee7a tam gi&aacute;c ABC n&ecirc;n&nbsp;<\/p><p><span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=\\overrightarrow{0}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$-\\overrightarrow{GC}=\\overrightarrow{GA}+\\overrightarrow{GB}=\\overrightarrow{a}+\\overrightarrow{b}$<\/span>.<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{CA}=\\overrightarrow{CG}+\\overrightarrow{GA}=-\\overrightarrow{GC}+\\overrightarrow{GA}=\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{a}=2\\overrightarrow{a}+\\overrightarrow{b}$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$\\overrightarrow{CA}=2\\overrightarrow{a}+\\overrightarrow{b}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 05:19:55","option_type":"math","len":0}]}
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