{"id":1020,"date":"2024-01-30T12:15:48","date_gmt":"2024-01-30T06:15:48","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=1020"},"modified":"2024-11-05T12:29:56","modified_gmt":"2024-11-05T06:29:56","slug":"common-tangent-of-two-circles","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/common-tangent-of-two-circles\/","title":{"rendered":"\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 (Common Tangent of Two Circles)"},"content":{"rendered":"<h2><span style=\"color: #339966;\">\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0995\u09af\u09bc\u099f\u09bf \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09a6\u09c1\u099f\u09bf <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.youtube.com\/watch?v=zkop3GyuFOA&amp;list=PLz2TLmgSzNOIUc7AjW9e9wIef-YqqyiVg\" target=\"_blank\" rel=\"noopener\">\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0<\/a><\/span> \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0995\u09df\u099f\u09bf \u09b9\u09ac\u09c7<\/span><i><span style=\"font-weight: 400;\">, <\/span><\/i><span style=\"font-weight: 400;\">\u09a4\u09be \u09ac\u09c3\u09a4\u09cd\u09a4 \u09a6\u09c1\u099f\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u0985\u09a8\u09cd\u09a4\u0983\u09b8\u09cd\u09a5 \u09ac\u09be \u09ac\u09b9\u09bf\u0983\u09b8\u09cd\u09a5\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09c7 \u0985\u09a5\u09ac\u09be \u099b\u09c7\u09a6 \u0995\u09b0\u09c7 \u0985\u09a5\u09ac\u09be \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09a8\u09be \u0995\u09b0\u09c7 \u09a4\u09be\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 : \u09a6\u09c1\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0-<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">\u0985\u09a8\u09cd\u09a4\u0983\u09b8\u09cd\u09a5\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09b2\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 <\/span><i><span style=\"font-weight: 400;\">\u09e7 <\/span><\/i><span style=\"font-weight: 400;\">\u099f\u09bf<\/span><i><\/i><\/li>\n<li><span style=\"font-weight: 400;\">\u09ac\u09b9\u09bf\u0983\u09b8\u09cd\u09a5\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09b2\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 <\/span><i><span style=\"font-weight: 400;\">\u09e9 <\/span><\/i><span style=\"font-weight: 400;\">\u099f\u09bf<\/span><\/li>\n<li><span style=\"font-weight: 400;\">\u099b\u09c7\u09a6 \u0995\u09b0\u09b2\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 <\/span><i><span style=\"font-weight: 400;\">\u09e8 <\/span><\/i><span style=\"font-weight: 400;\">\u099f\u09bf<\/span><\/li>\n<li><span style=\"font-weight: 400;\">\u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09a8\u09be \u0995\u09b0\u09b2\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 <\/span><i><span style=\"font-weight: 400;\">\u09ea <\/span><\/i><span style=\"font-weight: 400;\">\u099f\u09bf<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #339966;\"><strong>\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 (Common Tangent of Two Circles)<\/strong><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09a6\u09c1\u0987\u099f\u09bf <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/academic\/10\/\">\u09ac\u09c3\u09a4\u09cd\u09a4<\/a><\/span>\u0995\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09c7 \u09a4\u09ac\u09c7, \u09b0\u09c7\u0996\u09be\u099f\u09bf\u0995\u09c7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 <strong>\u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995<\/strong> \u09ac\u09b2\u09be \u09b9\u09df\u0964 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u09a6\u09c1\u0987 \u09a7\u09b0\u09a8\u09c7\u09b0 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09af\u09a5\u09be-<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09b8\u09b0\u09b2 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 (Direct common tangent)<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09a4\u09c0\u09b0\u09cd\u09af\u0995 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 (Transverse common tangent)<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/cp-algorithms.com\/geometry\/tangents-to-two-circles.png\" alt=\"\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0995\u09af\u09bc\u099f\u09bf\" width=\"472\" height=\"541\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a6\u09cd\u09ac\u09df \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b8\u0982\u09af\u09cb\u099c\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u098f\u0995\u0987 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a4\u09be\u0995\u09c7 <\/span><b>\u09b8\u09b0\u09b2 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995<\/b> <span style=\"font-weight: 400;\">\u098f\u09ac\u0982 \u09af\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a6\u09cd\u09ac\u09df \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u09b8\u0982\u09af\u09cb\u099c\u0995 \u09b0\u09c7\u0996\u09be\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a4\u09be\u0995\u09c7 <\/span><b>\u09a4\u09c0\u09b0\u09cd\u09af\u0995 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 <\/b><span style=\"font-weight: 400;\">\u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,<\/span><span style=\"font-weight: 400;\"> \u09b8\u09b0\u09b2 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09a6\u09cd\u09ac\u09df \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u099b\u09c7\u0964 \u09ac\u09c3\u09a4\u09cd\u09a4\u09a6\u09cd\u09ac\u09df\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <span class=\"katex-eq\" data-katex-display=\"false\">r_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">r_2<\/span><\/span><span style=\"font-weight: 400;\">;<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u0993\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">C_1T_1<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">C_2T_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b2\u09ae\u09cd\u09ac \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta PC_1T_1<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta PC_2T_2<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b8\u09a6\u09c3\u09b6\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\frac{PC_1}{PC_2}=\\frac{C_1T_1}{C_2T_2}=\\frac{r_1}{r_2}\\\\\n\n\\Rightarrow C_1P:C_2P=r_1:r_2<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">C_1C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u0982\u09b6\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">r_1:r_2<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u09ac\u09b9\u09bf\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">r_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">r_2<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u099a\u09cd\u099b\u09c7\u09a6\u09c0 \u09a8\u09df \u098f\u09ae\u09a8 \u09a6\u09c1\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09a4\u09c0\u09b0\u09cd\u09af\u0995 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09a6\u09cd\u09ac\u09df \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u099b\u09c7\u0964 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">C_1<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u0993\u09aa\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">C_1T_1<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">C_2T_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b2\u09ae\u09cd\u09ac \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta PC_1T_1<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta PC_2T_2<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b8\u09a6\u09c3\u09b6\u0964<\/span><\/li>\n<\/ul>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\frac{PC_1}{PC_2}=\\frac{C_1T_1}{C_2T_2}=\\frac{r_1}{r_2}\\\\\n\n\\Rightarrow C_1P:C_2P=r_1:r_2<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore P<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u099f\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">C_1C_2<\/span><\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u0982\u09b6\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">r_1:r_2<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u09ac\u09bf\u09ad\u0995\u09cd\u09a4 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09c7 \u0989\u09ad\u09df \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u0987<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09ac\u09b9\u09bf\u0983\u09b8\u09cd\u09a5 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><span style=\"font-weight: 400;\"> \u09b9\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964<\/span><\/p>\n<h2><span style=\"color: #339966;\"><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2+y^2=a^2<\/span><\/span><b> \u09ac\u09c3\u09a4\u09cd\u09a4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be <\/b><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">y=mx+c<\/span><\/span><b>\u00a0\u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b9\u09a4\u09c7 \u0996\u09a8\u09cd\u09a1\u09bf\u09a4 \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09df:<\/b><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">AB<\/span><\/span><span style=\"font-weight: 400;\"> \u0996\u09a8\u09cd\u09a1\u09bf\u09a4 \u099c\u09cd\u09af\u09be \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">(x_2,y_2)<\/span><\/span><span style=\"font-weight: 400;\">;<\/span><span style=\"font-weight: 400;\"> \u09a4\u09be\u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ad\u09c1\u099c\u09a6\u09cd\u09ac\u09df <span class=\"katex-eq\" data-katex-display=\"false\">(1+m^2)x^2+2mcx+c^2-a^2=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09c2\u09b2 \u09b9\u09a4\u09c7 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a7\u09b0\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ad\u09c1\u099c\u09a6\u09cd\u09ac\u09df \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0993<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span><\/span><span style=\"font-weight: 400;\">;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a4\u09be\u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">x_1+x_2=-\\frac{2mc}{1+m^2}<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">x_1x_2=\\frac{c^2-a^2}{1+m^2}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore (x_1-x_2)^2=(x_1+x_2)^2-4x_1x_2\\\\\n\n=\\frac{4m^2c^2}{(1+m^2)^2}-\\frac{4(c^2-a^2)}{1+m^2}\\\\\n\n=\\frac{4{a^2(1+m)^2-c^2}}{(1+m^2)^2}\u00a0<\/span>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7,<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">AB^2=(x_1-x_2)^2+(y_1-y_2)^2\\\\\n\n=(x_1-x_2)^2+(mx_1+c-mx_2-c)^2\\\\\n\n=(x_1-x_2)^2+m^2(x_1-x_2)^2\\\\\n\n=(1+m^2)(x_1-x_2)^2\\\\\n\n=(1+m^2)\\times 4\\frac{\\{a^2(1+m)^2-c^2\\}}{(1+m^2)^2}\\\\\n\n=4\\Big(a^2-\\frac{c^2}{1+m^2}\\Big)<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> \u09a8\u09bf\u09b0\u09cd\u09a3\u09c7\u09df \u0996\u09a8\u09cd\u09a1\u09bf\u09a4 \u099c\u09cd\u09af\u09be- \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af, <span class=\"katex-eq\" data-katex-display=\"false\">AB=2\\sqrt{\\Big(a^2-\\frac{c^2}{1+m^2}\\Big)}\\\\\n\n=2\\{(\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7)^2-(\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\\;\u00a0\u09b9\u09a4\u09c7\\;\u00a0\u099c\u09cd\u09af\u09be\\;\u00a0\u098f\u09b0\\;\u00a0\u09b2\u09ae\u09cd\u09ac\\;\u00a0\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac)^2\\}^{\\frac{1}{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">x^2+y^2+2gx+2fy+c=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09c3\u09a4\u09cd\u09a4 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09cb\u09a8\u09cb \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b9\u09a4\u09c7 \u0996\u09a8\u09cd\u09a1\u09bf\u09a4 \u099c\u09cd\u09af\u09be-\u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n<h2><span style=\"color: #339966;\"><b>\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u099c\u09cd\u09af\u09be-\u098f\u09b0<\/b><b>\u00a0<\/b><b> \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/b><span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><b> \u09b9\u09b2\u09c7 \u0989\u0995\u09cd\u09a4 \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <span class=\"katex-eq\" data-katex-display=\"false\">T=S_1<\/span><\/b><b>:<\/b><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf,<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"> \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <span class=\"katex-eq\" data-katex-display=\"false\">x^2+y^2+2gx+2fy+c=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0964 \u09ac\u09c3\u09a4\u09cd\u09a4\u099f\u09bf\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 <span class=\"katex-eq\" data-katex-display=\"false\">O(-g,\u00a0-f)<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">AB<\/span><\/span><span style=\"font-weight: 400;\"> \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><\/span><span style=\"font-weight: 400;\">\u0964 \u098f\u0996\u09be\u09a8\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">OP\\perp AB<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">OP<\/span><\/span><span style=\"font-weight: 400;\"> \u09b0\u09c7\u0996\u09be\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">AB<\/span><\/span><span style=\"font-weight: 400;\"> \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">y-y_1=\\frac{x_1+g}{y_1+f}(x-x_1)\\\\\n\n\\Rightarrow yy_1-y_1^2+fy-fy_1=-xx_1+x_1^2-gx+gx_1\\\\\n\n\\Rightarrow xx_1+yy_1+gx+gx_1+fy+fy_1+c=x_1^2+y_1^2+2gx_1+2fy_1+c\u00a0<\/span>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore x^2+y^2+2gx+2fy+c=0<\/span> \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <span class=\"katex-eq\" data-katex-display=\"false\">(x_1,y_1)<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09b2\u09c7 \u099c\u09cd\u09af\u09be\u099f\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3,<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">xx_1+yy_1+g(x+x_1)+f(y+y_1)+c=x_1^2+y_1^2+2gx_1+2fy_1+c<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u0982\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u0986\u0995\u09be\u09b0\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09df, <span class=\"katex-eq\" data-katex-display=\"false\">T=S_1<\/span><\/span><\/p>\n<p><b>\u09ac\u09bf.\u09a6\u09cd\u09b0.:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf <strong>\u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4, \u0985\u09a7\u09bf\u09ac\u09c3\u09a4\u09cd\u09a4, \u0989\u09aa\u09ac\u09c3\u09a4\u09cd\u09a4<\/strong> \u098f\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09cb\u099c\u09cd\u09af\u0964<\/span><span style=\"font-weight: 400;\">\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">d=OP=<\/span> \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u099c\u09cd\u09af\u09be \u098f\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">l<\/span><\/span><span style=\"font-weight: 400;\">=<\/span><span style=\"font-weight: 400;\">\u099c\u09cd\u09af\u09be \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">AP^2=OA^2-OP^2\\\\ \\Rightarrow (l\/2)^2=r^2-d^2 \\Rightarrow l=2\\sqrt{r^2-d^2}<\/span><\/span><\/li>\n<\/ul>\n<div class=\"x1tlxs6b x1g8br2z x1gn5b1j x230xth x14ctfv x1okitfd x6ikm8r x10wlt62 x1mzt3pk x1y1aw1k xn6708d xwib8y2 x1ye3gou x1n2onr6 x13faqbe x1vjfegm\" role=\"none\">\n<div class=\"\">\n<div class=\"x9f619 x1n2onr6 x1ja2u2z __fb-light-mode\" role=\"none\">\n<hr \/>\n<p dir=\"auto\" role=\"none\">\n<p class=\"x6prxxf x1fc57z9 x1yc453h x126k92a xzsf02u\" dir=\"auto\" role=\"none\"><em><strong>\u098f\u0987\u099a\u098f\u09b8\u09b8\u09bf \u0993 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be\u09b0\u09cd\u09a5\u09c0\u09a6\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<ul>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-25-online-batch-2-bangla-english-ict\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a \u09e8.\u09e6 (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-26-online-batch-bangla-english-ict\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2025-online-batch\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2026-online-batch\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/medical-admission-course\/\">\u09ae\u09c7\u09a1\u09bf\u0995\u09c7\u09b2 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-a-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-b-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/buet-ques-solve\/\">\u09ac\u09c1\u09df\u09c7\u099f \u0995\u09cb\u09b6\u09cd\u099a\u09c7\u09a8 \u09b8\u09b2\u09ad \u0995\u09cb\u09b0\u09cd\u09b8<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-a-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-b-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><em><strong>\u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u0995\u09bf\u09b2 \u09a1\u09c7\u09ad\u09c7\u09b2\u09aa\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/study-abroad-complete-guideline\/\">\u09ac\u09bf\u09a6\u09c7\u09b6\u09c7 \u0989\u099a\u09cd\u099a\u09b6\u09bf\u0995\u09cd\u09b7\u09be: Study Abroad Complete Guideline<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/student-hacks\/\">Student Hacks<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ielts-course\/\">IELTS Course by Munzereen Shahid<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/english-grammar-course\/\">Complete English Grammar Course<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ms-bundle\/\"> Microsoft Office 3 in 1 Bundle<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ghore-boshe-freelancing\/\">\u0998\u09b0\u09c7 \u09ac\u09b8\u09c7 Freelancing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/facebook-marketing\/\">Facebook Marketing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/adobe-4-in-1-bundle\/\">Adobe 4 in 1 Bundle<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em>\u09e7<\/em><em>\u09e6 \u09ae\u09bf\u09a8\u09bf\u099f \u09b8\u09cd\u0995\u09c1\u09b2\u09c7\u09b0 \u0995\u09cd\u09b2\u09be\u09b8\u0997\u09c1\u09b2\u09cb \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09a4\u09c7 \u09ad\u09bf\u099c\u09bf\u099f: <span style=\"color: #993300;\"><strong><a style=\"color: #993300;\" href=\"https:\/\/10minuteschool.com\/?ref=https%3A%2F%2Fblog.10minuteschool.com%2Fwordpress%2F&amp;post_id=78178&amp;blog_category_id=700\">www.10minuteschool.com<\/a><\/strong><\/span><\/em><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09a6\u09c1\u0987\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0995\u09af\u09bc\u099f\u09bf \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7? \u09a6\u09c1\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0995\u09df\u099f\u09bf \u09b9\u09ac\u09c7, \u09a4\u09be \u09ac\u09c3\u09a4\u09cd\u09a4 \u09a6\u09c1\u099f\u09bf \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u0985\u09a8\u09cd\u09a4\u0983\u09b8\u09cd\u09a5 \u09ac\u09be \u09ac\u09b9\u09bf\u0983\u09b8\u09cd\u09a5\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u0995\u09b0\u09c7 \u0985\u09a5\u09ac\u09be \u099b\u09c7\u09a6 \u0995\u09b0\u09c7 \u0985\u09a5\u09ac\u09be \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6 \u09a8\u09be \u0995\u09b0\u09c7 \u09a4\u09be\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 : \u09a6\u09c1\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4 \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0- \u0985\u09a8\u09cd\u09a4\u0983\u09b8\u09cd\u09a5\u09ad\u09be\u09ac\u09c7 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/common-tangent-of-two-circles\/\">Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4259,3037,50,3026],"tags":[891,90,889,892,888],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1020"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=1020"}],"version-history":[{"count":6,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1020\/revisions"}],"predecessor-version":[{"id":16117,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/1020\/revisions\/16117"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=1020"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=1020"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=1020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}