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{"save":1,"level":1,"time":"60","total":25,"point":5,"segment":[{"id":"10799","test_id":"727","question":"<p>Cho tam giác ABC có M, N l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB và BC. G\u1ecdi G là giao \u0111i\u1ec3m c\u1ee7a CM và AN. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây <strong>sai<\/strong>?<\/p>","options":["<strong>A.<\/strong> G là tr\u1ecdng tâm c\u1ee7a tam giác ABC.","<strong>B.<\/strong> G là tr\u1ef1c tâm c\u1ee7a tam giác ABC.","<strong>C.<\/strong> CG = 2GM.","<strong>D.<\/strong> BG \u0111i qua trung \u0111i\u1ec3m c\u1ee7a AC."],"correct":"2","answer":"<p>Câu <strong>sai <\/strong>là <span style=\"color:#16a085;\"><strong>B.<\/strong> G là tr\u1ef1c tâm c\u1ee7a tam giác ABC.<\/span><\/p><p><span class=\"svgedit\"><svg height=\"160\" width=\"250\"> <g>\\n<title><\/title>\\n<rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"252\" 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>\\n<title><\/title>\\n<g id=\"svg_20\"> <g id=\"svg_7\"> <g id=\"svg_4\"> <line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"16.41478\" x2=\"234.41478\" y1=\"139.79262\" y2=\"140\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"16.41478\" x2=\"92.41478\" y1=\"139.79262\" y2=\"18.79262\"><\/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\" x1=\"92.41478\" x2=\"233.41478\" y1=\"19.79261\" y2=\"139.79262\"><\/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=\"91.41478\" x2=\"124.41478\" y1=\"18.79262\" y2=\"138.79262\"><\/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=\"233.41478\" x2=\"54.41478\" y1=\"139.79262\" y2=\"77.79262\"><\/line> <\/g> <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=\"75.41478\" x2=\"70.41478\" y1=\"130.79262\" y2=\"146.79262\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"173.41478\" x2=\"168.41478\" y1=\"130.79262\" y2=\"146.79262\"><\/line> <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=\"71.41478\" x2=\"82.41478\" y1=\"37.79262\" y2=\"45.79262\"><\/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=\"69.41478\" x2=\"80.41478\" y1=\"40.79262\" y2=\"48.79262\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"36.41478\" x2=\"47.41478\" y1=\"94.79262\" y2=\"101.79262\"><\/line> <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=\"34.41478\" x2=\"45.41478\" y1=\"97.79262\" y2=\"104.79262\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"86.41478\" xml:space=\"preserve\" y=\"15.79262\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"3.41478\" xml:space=\"preserve\" y=\"149.79262\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"236.41478\" xml:space=\"preserve\" y=\"145.79262\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"39.41478\" xml:space=\"preserve\" y=\"77.79262\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"119.41478\" xml:space=\"preserve\" y=\"155.79262\">N<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" font-weight=\"bold\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"113.41478\" xml:space=\"preserve\" y=\"95.79262\">G<\/text> <\/g> <\/g> <\/svg><\/span><\/p><p>Vì M và N l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB và BC nên CM và AN là hai \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam giác ABC.<\/p><p>Mà CM và AN c\u1eaft nhau t\u1ea1i G nên G là tr\u1ecdng tâm c\u1ee7a tam giác ABC (A \u0111úng).<\/p><p>Suy ra <span class=\"math-tex\">$CG=\\dfrac{2}{3}CM$<\/span> ; <span class=\"math-tex\">$GM=\\dfrac{1}{3}CM$<\/span> hay <span class=\"math-tex\">$CG=2GM$<\/span> (C \u0111úng).<\/p><p>M\u1eb7t khác G là tr\u1ecdng tâm c\u1ee7a tam giác ABC nên BG là \u0111\u01b0\u1eddng trung tuy\u1ebfn th\u1ee9 ba. Suy ra BG \u0111i qua trung \u0111i\u1ec3m c\u1ee7a AC (D \u0111úng).<\/p><p><span style=\"color:#16a085;\"><strong>B sai<\/strong><\/span> vì tr\u1ef1c tâm là giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng cao, không ph\u1ea3i c\u1ee7a ba \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/p>","type":"choose","user_id":"131","test":"1","date":"2025-12-02 08:25:16"},{"id":"10800","test_id":"727","question":"<p>Gieo ng\u1eabu nhiên m\u1ed9t con xúc x\u1eafc cân \u0111\u1ed1i, \u0111\u1ed3ng ch\u1ea5t m\u1ed9t l\u1ea7n. Bi\u1ebfn c\u1ed1 nào sau \u0111ây có xác su\u1ea5t b\u1eb1ng 0?<\/p>","options":["<strong>A.<\/strong> E: "M\u1eb7t gieo \u0111\u01b0\u1ee3c có s\u1ed1 ch\u1ea5m l\u1edbn h\u01a1n 6".","<strong>B.<\/strong> F: "M\u1eb7t gieo \u0111\u01b0\u1ee3c có s\u1ed1 ch\u1ea5m nh\u1ecf h\u01a1n 3".","<strong>C.<\/strong> G: "M\u1eb7t gieo \u0111\u01b0\u1ee3c có s\u1ed1 ch\u1ea5m không l\u1edbn h\u01a1n 6".","<strong>D.<\/strong> H: "M\u1eb7t gieo \u0111\u01b0\u1ee3c có s\u1ed1 ch\u1ea5m là s\u1ed1 nguyên t\u1ed1"."],"correct":"1","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> E: "M\u1eb7t gieo \u0111\u01b0\u1ee3c có s\u1ed1 ch\u1ea5m l\u1edbn h\u01a1n 6".<\/span><\/p><p>Bi\u1ebfn c\u1ed1 E là bi\u1ebfn c\u1ed1 không th\u1ec3 nên có xác su\u1ea5t b\u1eb1ng 0.<\/p><p>Bi\u1ebfn c\u1ed1 F và bi\u1ebfn c\u1ed1 H là các bi\u1ebfn c\u1ed1 ng\u1eabu nhiên nên có xác su\u1ea5t l\u1edbn h\u01a1n 0 và nh\u1ecf h\u01a1n 1.<\/p><p>Bi\u1ebfn c\u1ed1 G là bi\u1ebfn c\u1ed1 ch\u1eafc ch\u1eafn nên có xác su\u1ea5t b\u1eb1ng 1.<\/p>","type":"choose","user_id":"131","test":"1","date":"2025-12-02 08:25:27"}]}