Vị trí tương đối của hai đường tròn

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 17. Vị trí tương đối của hai đường trònBài tập trung bình

{"common":{"save":0,"post_id":"7940","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8434","post_id":"7940","mon_id":"1159278","chapter_id":"1159329","question":"Xác \u0111\u1ecbnh v\u1ecb trí t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng tròn (I ; 10) và (J ; 5) bi\u1ebft IJ = 6.<\/p>","options":["A.<\/strong> ngoài nhau","B.<\/strong> ti\u1ebfp xúc ngoài","C.<\/strong> \u0111\u1ef1ng nhau","D.<\/strong> c\u1eaft nhau"],"correct":"4","level":"2","hint":"","answer":"Ch\u1ecdn D.<\/strong> c\u1eaft nhau.<\/span><\/p>Vì 10 – 5 < 6 < 10 + 5 hay R – R' < IJ < R + R' nên hai \u0111\u01b0\u1eddng tròn c\u1eaft nhau.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-08 01:26:10","option_type":"txt","len":2},{"id":"8438","post_id":"7940","mon_id":"1159278","chapter_id":"1159329","question":"Cho \u0111\u01b0\u1eddng tròn tâm O, bán kính R. L\u1ea5y \u0111i\u1ec3m A tùy ý trên \u0111\u01b0\u1eddng tròn (O ; R). V\u1ebd \u0111\u01b0\u1eddng tròn tâm O' \u0111\u01b0\u1eddng kính OA. Khi \u0111ó .<\/p>","options":["A.<\/strong> (O) và (O') ti\u1ebfp xúc trong t\u1ea1i A.","B.<\/strong> (O) và (O') ti\u1ebfp xúc ngoài t\u1ea1i A.","C.<\/strong> (O) và (O') không giao nhau.","D.<\/strong> (O) và (O') c\u1eaft nhau t\u1ea1i A và O'."],"correct":"1","level":"2","hint":"","answer":"Ch\u1ecdn A.<\/strong> (O) và (O') ti\u1ebfp xúc trong t\u1ea1i A.<\/span><\/p><svg height=\"210\" width=\"230\"> <g><title><\/title><rect fill=\"#aaffff\" height=\"212\" id=\"canvas_background\" width=\"232\" 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><ellipse cx=\"107\" cy=\"105.25\" fill=\"#fff\" id=\"svg_1\" rx=\"100\" ry=\"100\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"157\" cy=\"105\" fill=\"#fff\" id=\"svg_2\" rx=\"50\" ry=\"50\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"107\" cy=\"105.25\" fill=\"#000000\" id=\"svg_3\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"157\" cy=\"105\" fill=\"#000000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"207\" cy=\"105\" fill=\"#000000\" id=\"svg_5\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"106\" x2=\"209\" y1=\"105.25\" y2=\"105\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"89\" xml:space=\"preserve\" y=\"112.25\">O<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"210\" xml:space=\"preserve\" y=\"111.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"150\" xml:space=\"preserve\" y=\"126.25\">O'<\/text> <\/g> <\/svg><\/span><\/p>Ta có O' là trung \u0111i\u1ec3m c\u1ee7a OA và bán kính \u0111\u01b0\u1eddng tròn (O') là R' = $\\dfrac{OA}{2}=\\dfrac{R}{2}$<\/span>.<\/p>\u0110\u1ed9 dài \u0111o\u1ea1n n\u1ed1i tâm OO' $=\\dfrac{OA}{2}=\\dfrac{R}{2}$<\/span>. Ta có R – R' = $\\dfrac{R}{2}$<\/span> = OO' nên (O) và (O') ti\u1ebfp xúc trong t\u1ea1i A.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-08 01:36:48","option_type":"txt","len":3},{"id":"8441","post_id":"7940","mon_id":"1159278","chapter_id":"1159329","question":"Cho hai \u0111\u01b0\u1eddng tròn (O) và (O') ti\u1ebfp xúc ngoài v\u1edbi nhau t\u1ea1i A. M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng qua A c\u1eaft (O) t\u1ea1i B và c\u1eaft (O') t\u1ea1i C. Xét v\u1ecb trí t\u01b0\u01a1ng \u0111\u1ed1i hai \u0111\u01b0\u1eddng th\u1eb3ng OB và O’C.<\/p>","options":["A.<\/strong> c\u1eaft nhau","B.<\/strong> song song","C.<\/strong> vuông góc","D.<\/strong> trùng nhau"],"correct":"2","level":"2","hint":"","answer":"Ch\u1ecdn B.<\/strong> song song.<\/span><\/p><svg height=\"210\" width=\"330\"> <g><title><\/title><rect fill=\"#aad4ff\" height=\"212\" id=\"canvas_background\" width=\"332\" 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><ellipse cx=\"103.5\" cy=\"105.25\" fill=\"#fff\" id=\"svg_1\" rx=\"100\" ry=\"100\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"264\" cy=\"105.25\" fill=\"#fff\" id=\"svg_2\" rx=\"60\" ry=\"60\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"103.5\" cy=\"105.25\" fill=\"#000000\" id=\"svg_3\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"264\" cy=\"105.25\" fill=\"#000000\" id=\"svg_4\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"204\" cy=\"105.25\" fill=\"#ff0000\" id=\"svg_5\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"47.00001\" x2=\"299\" y1=\"23.25\" y2=\"154.25\"><\/line> <ellipse cx=\"47.5\" cy=\"23.25\" fill=\"#ff0000\" id=\"svg_7\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"298\" cy=\"154\" fill=\"#ff0000\" id=\"svg_8\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"47\" x2=\"105\" y1=\"24.25\" y2=\"105.25\"><\/line> <line fill=\"none\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"102\" x2=\"264\" y1=\"105.25\" y2=\"105\"><\/line> <line fill=\"none\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"264\" x2=\"299\" y1=\"105.25\" y2=\"152.25\"><\/line> <text fill=\"#000000\" 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\" xml:space=\"preserve\" y=\"129.25\">O<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"182\" xml:space=\"preserve\" y=\"124.25\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"265\" xml:space=\"preserve\" y=\"100.25\">O'<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"31\" xml:space=\"preserve\" y=\"21.25\">B<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"290\" xml:space=\"preserve\" y=\"177.25\">C<\/text> <\/g> <\/svg><\/span><\/p>Xét $\\triangle$<\/span>OBA cân t\u1ea1i O nên $\\widehat{OBA}=\\widehat{OAB}$<\/span>.<\/p>Xét $\\triangle$<\/span>O'CA cân t\u1ea1i O' nên $\\widehat{O^\\prime CA}=\\widehat{O^\\prime AC}$<\/span>.<\/p>Mà $\\widehat{OAB}=\\widehat{O^\\prime AC}$<\/span>(hai góc \u0111\u1ed1i \u0111\u1ec9nh) nên $\\widehat{OBA}=\\widehat{O^\\prime CA}$<\/span>.<\/p>Mà hai góc này \u1edf v\u1ecb trí so le trong nên suy ra OB \/\/ O'C..<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-08 01:48:34","option_type":"txt","len":2}]}