{"common":{"save":0,"post_id":"6395","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6187","mon_id":"1158767","chapter_id":"1158861","post_id":"6395","question":"<p>Cho \u25b3ABC c&oacute; M, N l\u1ea7n l\u01b0\u1ee3t l&agrave; trung \u0111i\u1ec3m c\u1ee7a BC v&agrave; AC. G\u1ecdi G l&agrave; giao \u0111i\u1ec3m c\u1ee7a AM v&agrave; BN . Kh\u1eb3ng \u0111\u1ecbnh n&agrave;o sau \u0111&acirc;y \u0111&uacute;ng?<\/p>","options":["A. <span class=\"math-tex\">$\\overrightarrow{AG}=\\overrightarrow{AB}+\\overrightarrow{AC}$<\/span>.","B. <span class=\"math-tex\">$\\overrightarrow{AG}=2(\\overrightarrow{AB}+\\overrightarrow{AC})$<\/span> .","C. <span class=\"math-tex\">$\\overrightarrow{AG}=\\frac{1}{3}\\left(\\overrightarrow{AB}+\\overrightarrow{AC}\\right)$<\/span>.","D. <span class=\"math-tex\">$\\overrightarrow{AG}=\\frac{2}{3}\\left(\\overrightarrow{AB}+\\overrightarrow{AC}\\right)$<\/span>. "],"correct":"3","level":"2","hint":"","answer":"<p><span style=\"color:#27ae60;\"><strong>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave; <\/strong>C. <span class=\"math-tex\">$\\overrightarrow{AG}=\\frac{1}{3}\\left(\\overrightarrow{AB}+\\overrightarrow{AC}\\right)$<\/span>.<\/span><\/p><p><span class=\"svgedit\"><svg height=\"227\" width=\"325\"> <g> &lt;title&gt;&lt;\/title&gt; <rect fill=\"#fff\" height=\"229\" id=\"canvas_background\" width=\"327\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" wfd-invisible=\"true\" 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&gt; <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"3\" x1=\"111.50001\" x2=\"28.50001\" y1=\"18.43466\" y2=\"196.43467\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"3\" x1=\"110.50001\" x2=\"297.50002\" y1=\"17.93467\" y2=\"198.93467\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"3\" x1=\"27.50001\" x2=\"296.50001\" y1=\"197.93467\" y2=\"197.93467\"><\/line> <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\" transform=\"matrix(1.208336925706881,0,0,1,-16.082477077222507,0) \" x=\"15.69585\" xml:space=\"preserve\" y=\"205.93466\">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\" style=\"cursor: move;\" text-anchor=\"start\" transform=\"matrix(1.208336925706881,0,0,1,-16.082477077222507,0) \" x=\"262.31581\" xml:space=\"preserve\" y=\"203.93466\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"matrix(1.208336925706881,0,0,1,-16.082477077222507,0) \" x=\"96.79906\" xml:space=\"preserve\" y=\"18.93466\">A<\/text> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"112.00001\" x2=\"168.00001\" y1=\"19.93466\" y2=\"196.93467\"><\/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=\"158.00001\" xml:space=\"preserve\" y=\"218.93467\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-44.126007080078125 212.671890258789,94.75284576416014) \" x=\"204.00001\" xml:space=\"preserve\" y=\"102.93467\">N<\/text> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"30.00002\" x2=\"199.00001\" y1=\"195.93467\" y2=\"103.93467\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"161.00001\" xml:space=\"preserve\" y=\"148.93467\">G<\/text> <ellipse cx=\"147.50001\" cy=\"131.93466\" fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" rx=\"1.5\" ry=\"1\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"3\"><\/ellipse> <\/g> <\/svg><\/span><\/p><p>V&igrave; M, N l&agrave; trung \u0111i\u1ec3m c\u1ee7a BC v&agrave; AC n&ecirc;n AM, BN l&agrave; c&aacute;c \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi&aacute;c ABC.&nbsp;<br \/>M&agrave; G l&agrave; giao \u0111i\u1ec3m c\u1ee7a AM v&agrave; BN n&ecirc;n G l&agrave; tr\u1ecdng t&acirc;m c\u1ee7a tam gi&aacute;c ABC.<br \/>Suy ra&nbsp; <span class=\"math-tex\">$\\Rightarrow\\overrightarrow{AG}=\\frac{2}{3}\\overrightarrow{AB}$<\/span>&nbsp; (1)<br \/>M\u1eb7t kh&aacute;c, v&igrave; M l&agrave; trung \u0111i\u1ec3m c\u1ee7a BC n&ecirc;n&nbsp;<span class=\"math-tex\">$\\Rightarrow\\overrightarrow{AM}=\\frac{1}{2}(\\overrightarrow{AB}+\\overrightarrow{AC})$<\/span> &nbsp;(2)<br \/>K\u1ebft h\u1ee3p (1) v&agrave; (2) ta c&oacute;<br \/><span class=\"math-tex\">$\\overrightarrow{AG}=\\frac{2}{3}\\overrightarrow{AM}$<\/span><\/p><p>&nbsp; &nbsp; &nbsp;&nbsp;<span class=\"math-tex\">$=\\frac{2}{3}.\\frac{1}{2}(\\overrightarrow{AB}+\\overrightarrow{AC})$<\/span><\/p><p>&nbsp; &nbsp; &nbsp;&nbsp;<span class=\"math-tex\">$=\\frac{1}{3}(\\overrightarrow{AB}+\\overrightarrow{AC})$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 06:05:01","option_type":"math","len":0},{"id":"6188","mon_id":"1158767","chapter_id":"1158861","post_id":"6395","question":"<p>Cho 5 \u0111i\u1ec3m ph&acirc;n bi\u1ec7t &nbsp;<span class=\"math-tex\">$M,N,P,Q,R$<\/span> . M\u1ec7nh \u0111\u1ec1 n&agrave;o sau \u0111&acirc;y \u0111&uacute;ng?<\/p>","options":["A. <span class=\"math-tex\">$\\overrightarrow{MN}+\\overrightarrow{PQ}+\\overrightarrow{RN}+\\overrightarrow{NP}+\\overrightarrow{QR}=\\overrightarrow{MP}$<\/span> .","B. <span class=\"math-tex\">$\\overrightarrow{MN}+\\overrightarrow{PQ}+\\overrightarrow{RN}+\\overrightarrow{NP}+\\overrightarrow{QR}=\\overrightarrow{PR}$<\/span> .","C. <span class=\"math-tex\">$\\overrightarrow{MN}+\\overrightarrow{PQ}+\\overrightarrow{RN}+\\overrightarrow{NP}+\\overrightarrow{QR}=\\overrightarrow{MR}$<\/span>.","D. <span class=\"math-tex\">$\\overrightarrow{MN}+\\overrightarrow{PQ}+\\overrightarrow{RN}+\\overrightarrow{NP}+\\overrightarrow{QR}=\\overrightarrow{MN}$<\/span>. "],"correct":"4","level":"2","hint":"<p><span class=\"math-tex\">$\\overrightarrow{MN}+\\overrightarrow{PQ}+\\overrightarrow{RN}+\\overrightarrow{NP}+\\overrightarrow{QR}=\\left(\\overrightarrow{MN}+\\overrightarrow{NP}\\right)+\\left(\\overrightarrow{PQ}+\\overrightarrow{QR}\\right)+\\overrightarrow{RN}=\u200b\u200b\\overrightarrow{MP}\\\\\\left(\\overrightarrow{MP}+\\overrightarrow{PR}\\right)+\\overrightarrow{RN}=\\overrightarrow{MR}+\\overrightarrow{RN}=\\overrightarrow{MN}$<\/span><\/p>","answer":"<p><span style=\"color:#27ae60;\"><strong>\u0110&aacute;p &aacute;n D<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 06:10:50","option_type":"math","len":0},{"id":"6189","mon_id":"1158767","chapter_id":"1158861","post_id":"6395","question":"<p>Cho h&igrave;nh b&igrave;nh h&agrave;nh <span class=\"math-tex\">$ABCD$<\/span>&nbsp;, \u0111\u1eb3ng th\u1ee9c v&eacute;c t\u01a1 n&agrave;o sau \u0111&acirc;y \u0111&uacute;ng?<\/p>","options":["A. <span class=\"math-tex\">$\\overrightarrow{CD}+\\overrightarrow{CB}=\\overrightarrow{CA}$<\/span> .","B. <span class=\"math-tex\">$\\overrightarrow{AB}+\\overrightarrow{AC}=\\overrightarrow{AD}$<\/span>.","C. <span class=\"math-tex\">$\\overrightarrow{BA}+\\overrightarrow{BD}=\\overrightarrow{BC}$<\/span>.","D. <span class=\"math-tex\">$\\overrightarrow{CD}+\\overrightarrow{AD}=\\overrightarrow{AC}$<\/span>. "],"correct":"1","level":"2","hint":"<p><span class=\"svgedit\"><svg height=\"131\" width=\"249\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"133\" id=\"canvas_background\" width=\"251\" 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=\"131\" id=\"svg_1\" width=\"249\" x=\"0\" xlink:href=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAACDCAMAAAB4KE0FAAABYlBMVEX\/\/\/8AAIDX19+fn79YWKAAAAD7+\/tDQ5gjI4zy8vPi4ucMDISursdra6j\/AADKytePj7j5+fnc4+Z3WEMTEy6ZrL1MIiLv8vLy8u\/CztkiIkzm49y9rJlefpcuExPn6+zo6OmXfl5+AQHi4uHZzsL29vft7e6enZ1DWHdGOTk3KSkxGRkMAwfHAADs6ufW1te6uriEhLPGt6+Yj481TF0rFRUhExQUCAzlAADR0dvExNPR0dG9vc+5xs22tsvNxrmqrrKqpqZ3hJCAdnYAAHRdXW1nWVkMClAmPz9dTDUOACM9GBhnERFjDg8nAglwBwhqAQTzAADXAADc3NPOzMzExMSnp8O9vb2YmLyZma1OTpyQkJutpI6MiIgXF4hJSYd5aXkbG3iQhHdcWXFOTmp2aGgAAGQzM2KDdVJQUFAEAD4uGCo\/PyYmGh1MFxdbFRU1BguPBgbPAAC3AACfAACPAADT3C\/aAAADZUlEQVR42u2dV2\/iQBSFj5MMhGbwZumEmkZL7733bMr23ntv\/3\/toAie47F0Z+d+Ekh+Qb76hrmDj5gBwzAMwzAMowVWn3DYSUI77NLT9qsf2pHNZ5IoiTi0Iyf6rUmxaUE7SkKImzegFpVdIabHH8INqUQmafWpNditV2KkgNGEu5seECOW\/ZZRaG6\/mo8nXY3U1tyWU6pyOXc7mrC\/42t5lUZ7KiGlBYtLPq5AHbJ5kYaWZPPKtSJpo73lfNyCLHxDoE6xNcNNFzA6JU\/8VGO2Srv2sdmZuTsA1r4Ip3hZbBybZrPmA12K9Xnz\/KgC2dR+maZ5651Bl09l+w7\/PoVsqk2n8uc9dHl\/Zt9heRiyWfoxf\/5zF4QZnP1tNusByCa412hsUf6aw\/fyUFQrkE7ECIM2YSMCDwgavaSFA75eIwgP8OuqPGr4QRvvlEdBG1YO3ZTHdFUeCIUCaKGd8hg8YFVX5fbksQDadChXoF8ooTwI2mirfEhb5RGjG5foptyjn5EBFZSH2xfkV4UKKA+FiqBNp3L6\/UIJ5QHQRlvlC9oq9xuL8IAJ8so9enIQNBRQHoUHRPRVTj1c6FSuQL9g5az8+oR1Ve7Vk4NHCij3JlzQVrnfWAVtOEIEVOgXrNw9g9oqjxkT8IBl8so9y5MUUB5rX5BfFSqhvAu00TZC5NQY0Ex5sFM5\/SWCRCLGvfYFR4gSJg8FlHNqDPr9Qgnl1MMFVq6d8minco4QOUJk5ddQ\/gC04QjRgX6\/YOXu8XmkvIe88rDRg0uUWCKA\/sMijf94qq\/yZdBG2wiRU2PJLJJXHnjWqVyvCHECbThC1EI5p8YSuTu8RzxcKA6\/2fZA+db38tln0su3sXq5PDcG2VSOTNM8fd1NmLl507yoQTb3T+zK\/xwadNlumDYCsinO2B978riLMF8vTLNZhTxKaThszJS\/vQVlKvXT49oQpJET6auZcwm0CayPD0IaA0LT\/WCzOwd67gebelHoU6vy1nkR++sWXGFNFVIJtSqH9UHErZIYcVd6Sai3Eb9lD9LWzsUumFwBlHOezdu6XR4S8iSu4o7XORGH28pFJuk0NaX24W8NdqQSKu2hL2uwO6IGVJud5BwL4yjXb\/nlnIGE2wf6jXUIh\/3NAhiGYRiGYRjmf+cfYh1Rp50vRyQAAAAASUVORK5CYII=\" y=\"0\"><\/image> <\/g> <\/svg><\/span><\/p>","answer":"<p><span style=\"color:#27ae60;\"><strong>\u0110&aacute;p &aacute;n A<\/strong><\/span> ( theo quy t\u1eafc h&igrave;nh b&igrave;nh h&agrave;nh)<\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 06:14:41","option_type":"math","len":0}]}