Mở đầu về đường tròn

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 13. Mở đầu về đường trònBài tập trung bình

{"common":{"save":0,"post_id":"7913","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8228","post_id":"7913","mon_id":"1159278","chapter_id":"1159329","question":"Cho hình vuông ABCD có c\u1ea1nh b\u1eb1ng 4 cm. Khi \u0111ó 4 \u0111i\u1ec3m A, B, C, D cùng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tròn bán kính b\u1eb1ng<\/p>","options":["A.<\/strong> 2 cm","B.<\/strong> 4 cm","C.<\/strong> $4\\sqrt{2}$<\/span> cm","D.<\/strong> $2\\sqrt{2}$<\/span> cm"],"correct":"4","level":"2","hint":"","answer":"Ch\u1ecdn D.<\/strong> $2\\sqrt{2}$<\/span> cm.<\/span><\/p><svg height=\"210\" width=\"210\"> <g> <title><\/title> <rect fill=\"none\" height=\"212\" id=\"canvas_background\" width=\"212\" 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> <title><\/title> <rect fill=\"none\" height=\"160\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" width=\"160\" x=\"27.16666\" y=\"26.25\"><\/rect> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"28.16667\" x2=\"186.5\" y1=\"26.91669\" y2=\"186.25\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" transform=\"rotate(90 107.33332824707031,106.58334350585939) \" x1=\"28.16667\" x2=\"186.5\" y1=\"26.91669\" y2=\"186.25\"><\/line> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"15.3332\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(45 107.33237457275388,95.83380126953126) \" width=\"14.66654\" x=\"99.9991\" y=\"88.16722\"><\/rect> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"21\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"11.99989\" xml:space=\"preserve\" y=\"24.16779\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"21\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"186.665\" xml:space=\"preserve\" y=\"24.83445\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"21\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"187.33166\" xml:space=\"preserve\" y=\"198.83289\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"21\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"13.99987\" xml:space=\"preserve\" y=\"202.1662\">D<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"21\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"98.66578\" xml:space=\"preserve\" y=\"128.83352\">O<\/text> <\/g> <\/svg><\/span><\/p>G\u1ecdi O là giao \u0111i\u1ec3m c\u1ee7a AC và BD suy ra OA = OB = OC = OD, suy ra A, B, C, D cùng thu\u1ed9c \u0111\u01b0\u1eddng tròn (O ; OA).<\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí Pythagore vào tam giác ADC vuông t\u1ea1i D có: AC² = AD² + DC² = 4² + 4² = 32.<\/p>Suy ra AC = $4\\sqrt{2}$<\/span> cm. Suy ra OA = $2\\sqrt{2}$<\/span> (cm).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-01 02:24:43","option_type":"math","len":0},{"id":"8230","post_id":"7913","mon_id":"1159278","chapter_id":"1159329","question":"Cho hình ch\u1eef nh\u1eadt ABCD có AB = 12 cm, BC = 5 cm. B\u1ed1n \u0111i\u1ec3m A , B , C , D cùng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tròn bán kính b\u1eb1ng<\/p>","options":["A.<\/strong> 13 cm","B.<\/strong> 6,5 cm","C.<\/strong> 12 cm","D.<\/strong> 6 cm"],"correct":"2","level":"2","hint":"","answer":"Ch\u1ecdn B.<\/strong> 6,5 cm.<\/span><\/p>G\u1ecdi O là giao \u0111i\u1ec3m c\u1ee7a AC và BD suy ra OA = OB = OC = OD, suy ra A, B, C, D cùng thu\u1ed9c \u0111\u01b0\u1eddng tròn (O ; OA).<\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí Pythagore vào tam giác ADC vuông t\u1ea1i D có:<\/p>AC² = AD² + DC² = 5² + 12² = 169.<\/p>Suy ra AC = 13 cm. Suy ra OA = 6,5 (cm).<\/p><svg height=\"180\" width=\"270\"> <g> <title><\/title> <rect fill=\"none\" height=\"182\" id=\"canvas_background\" width=\"272\" 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> <title><\/title> <rect fill=\"none\" height=\"136\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" width=\"214\" x=\"28\" y=\"24.25\"><\/rect> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"28\" x2=\"243\" y1=\"25.25\" y2=\"160.25\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"241\" x2=\"28\" y1=\"24.25\" y2=\"160.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"7\" xml:space=\"preserve\" y=\"28.25\">A<\/text> <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=\"246\" xml:space=\"preserve\" y=\"22.25\">B<\/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=\"247\" xml:space=\"preserve\" y=\"170.25\">C<\/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=\"8\" xml:space=\"preserve\" y=\"174.25\">D<\/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=\"127\" xml:space=\"preserve\" y=\"81.25\">O<\/text> <\/g> <\/svg><\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-01 02:28:13","option_type":"txt","len":0},{"id":"8232","post_id":"7913","mon_id":"1159278","chapter_id":"1159329","question":"Cho tam giác ABC vuông t\u1ea1i A, AB = 6 cm, AC = 8 cm. Bán kính \u0111\u01b0\u1eddng tròn \u0111i qua ba \u0111i\u1ec3m A, B, C là<\/p>","options":["A.<\/strong> 10 cm","B.<\/strong> 20 cm","C.<\/strong> 5 cm","D.<\/strong> 15 cm"],"correct":"3","level":"2","hint":"","answer":"Ch\u1ecdn C.<\/strong> 5 cm.<\/span><\/p>G\u1ecdi M là trung \u0111i\u1ec3m c\u1ee7a BC. Vì tam giác ABC vuông t\u1ea1i A có M là trung \u0111i\u1ec3m c\u1ea1nh huy\u1ec1n BC.<\/p>Suy ra MA = MB = MC = $\\dfrac{1}{2}$<\/span>BC.<\/p>Suy ra M là tâm \u0111\u01b0\u1eddng tròn \u0111i qua ba \u0111i\u1ec3m A, B, C.<\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí Pythagore vào tam giác ABC vuông t\u1ea1i A có: <\/p>BC² = AB² + AC² = 6² + 8² = 100. Suy ra BC = 10 cm, suy ra MA = 5 cm.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-01 02:37:02","option_type":"txt","len":0}]}