{"id":567266,"date":"2026-07-22T09:20:10","date_gmt":"2026-07-22T02:20:10","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567266"},"modified":"2026-07-22T11:01:23","modified_gmt":"2026-07-22T04:01:23","slug":"duong-tron-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/duong-tron-la-gi\/","title":{"rendered":"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? Y\u1ebfu t\u1ed1, chu vi, di\u1ec7n t\u00edch v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh"},"content":{"rendered":"<p style=\"text-align: justify;\"><b>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? <\/b>\u0110\u01b0\u1eddng tr\u00f2n <span style=\"font-weight: 400;\">t\u00e2m O b\u00e1n k\u00ednh R l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00e1ch \u0111i\u1ec3m O c\u1ed1 \u0111\u1ecbnh m\u1ed9t kho\u1ea3ng kh\u00f4ng \u0111\u1ed5i b\u1eb1ng R. \u0110\u01b0\u1eddng tr\u00f2n l\u00e0 h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n, xu\u1ea5t hi\u1ec7n xuy\u00ean su\u1ed1t ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THCS v\u00e0 THPT. B\u00e0i vi\u1ebft n\u00e0y tr\u00ecnh b\u00e0y \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec, c\u00e1c y\u1ebfu t\u1ed1, c\u00f4ng th\u1ee9c chu vi \u2013 di\u1ec7n t\u00edch, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n, v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i, g\u00f3c \u1edf t\u00e2m \u2013 g\u00f3c n\u1ed9i ti\u1ebfp v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec?<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh R (k\u00fd hi\u1ec7u (O; R)) l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch t\u00e2m O m\u1ed9t kho\u1ea3ng b\u1eb1ng R. C\u1ea7n ph\u00e2n bi\u1ec7t: \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 \u0111\u01b0\u1eddng cong kh\u00e9p k\u00edn (ch\u1ec9 g\u1ed3m c\u00e1c \u0111i\u1ec3m n\u1eb1m tr\u00ean vi\u1ec1n, c\u00f3 chu vi), c\u00f2n h\u00ecnh tr\u00f2n l\u00e0 ph\u1ea7n m\u1eb7t ph\u1eb3ng n\u1eb1m b\u00ean trong \u0111\u01b0\u1eddng tr\u00f2n k\u1ec3 c\u1ea3 vi\u1ec1n (c\u00f3 di\u1ec7n t\u00edch).<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-568725\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-1.jpg\" alt=\"duong-tron-la-gi-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>C\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 n\u1ed9i dung gi\u00fap ng\u01b0\u1eddi h\u1ecdc l\u00e0m quen v\u1edbi nh\u1eefng th\u00e0nh ph\u1ea7n c\u01a1 b\u1ea3n trong h\u00ecnh h\u1ecdc. Ph\u1ea7n n\u00e0y kh\u00e1i qu\u00e1t c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m, m\u1ed1i li\u00ean h\u1ec7 v\u00e0 t\u00ednh ch\u1ea5t li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n. Qua \u0111\u00f3, ng\u01b0\u1eddi h\u1ecdc c\u00f3 th\u1ec3 x\u00e2y d\u1ef1ng n\u1ec1n t\u1ea3ng \u0111\u1ec3 ti\u1ebfp c\u1eadn c\u00e1c ki\u1ebfn th\u1ee9c h\u00ecnh h\u1ecdc n\u00e2ng cao h\u01a1n.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Y\u1ebfu t\u1ed1<\/b><\/td>\n<td><b>\u0110\u1ecbnh ngh\u0129a<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">T\u00e2m<\/span><\/td>\n<td><span style=\"font-weight: 400;\">\u0110i\u1ec3m O c\u1ed1 \u0111\u1ecbnh, c\u00e1ch \u0111\u1ec1u m\u1ecdi \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">B\u00e1n k\u00ednh (R)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng k\u00ednh (d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">D\u00e2y cung \u0111i qua t\u00e2m, d = 2R (d\u00e2y l\u1edbn nh\u1ea5t)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">D\u00e2y cung<\/span><\/td>\n<td><span style=\"font-weight: 400;\">\u0110o\u1ea1n th\u1eb3ng n\u1ed1i hai \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Cung<\/span><\/td>\n<td><span style=\"font-weight: 400;\">M\u1ed9t ph\u1ea7n c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n gi\u1edbi h\u1ea1n b\u1edfi hai \u0111i\u1ec3m<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Ti\u1ebfp tuy\u1ebfn<\/span><\/td>\n<td><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng th\u1eb3ng ch\u1ec9 c\u00f3 m\u1ed9t \u0111i\u1ec3m chung v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: justify;\"><b>C\u00f4ng th\u1ee9c chu vi v\u00e0 di\u1ec7n t\u00edch \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh chu vi \u0111\u01b0\u1eddng tr\u00f2n:<\/span><b> C = 2\u03c0R = \u03c0d<\/b><span style=\"font-weight: 400;\">. Trong \u0111\u00f3:<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">C: Chu vi \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">R: B\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d: \u0110\u01b0\u1eddng k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u03c0 \u2248 3,14.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n: <\/span><b>S = \u03c0R\u00b2<\/b><span style=\"font-weight: 400;\">. Trong \u0111\u00f3:<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">S: Di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">R: B\u00e1n k\u00ednh h\u00ecnh tr\u00f2n.<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-568726\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-2.jpg\" alt=\"duong-tron-la-gi-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m I(a; b) b\u00e1n k\u00ednh R c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><\/p>\n<p style=\"text-align: justify;\"><b>(x \u2212 a)\u00b2 + (y \u2212 b)\u00b2 = R\u00b2<\/b><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Khi t\u00e2m tr\u00f9ng g\u1ed1c t\u1ecda \u0111\u1ed9 O(0; 0), ph\u01b0\u01a1ng tr\u00ecnh r\u00fat g\u1ecdn th\u00e0nh x\u00b2 + y\u00b2 = R\u00b2.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 m\u1ed9t trong c\u00e1c \u0111\u01b0\u1eddng conic quen thu\u1ed9c c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n ph\u1ed5 th\u00f4ng, b\u00ean c\u1ea1nh <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/parabol\/\">parabol<\/a> \u2014 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc hai y = ax\u00b2 + bx + c.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\"><b>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? <\/b>G\u1ecdi d l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m O c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng, R l\u00e0 b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu d &gt; R: \u0110\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu d = R: \u0110\u01b0\u1eddng th\u1eb3ng ti\u1ebfp x\u00fac v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i m\u1ed9t \u0111i\u1ec3m (\u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu d &lt; R: \u0110\u01b0\u1eddng th\u1eb3ng c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t.<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">X\u00e9t hai \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 b\u00e1n k\u00ednh R v\u00e0 r (R \u2265 r). G\u1ecdi OO&#8217; l\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa hai t\u00e2m c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu OO&#8217; &gt; R + r: Hai \u0111\u01b0\u1eddng tr\u00f2n \u1edf ngo\u00e0i nhau, kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu OO&#8217; = R + r: Hai \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac ngo\u00e0i, c\u00f3 m\u1ed9t \u0111i\u1ec3m chung.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu R \u2212 r &lt; OO&#8217; &lt; R + r: Hai \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">N\u1ebfu OO&#8217; = R \u2212 r: Hai \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac trong, c\u00f3 m\u1ed9t \u0111i\u1ec3m chung.<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-568727\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-3.jpg\" alt=\"duong-tron-la-gi-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>G\u00f3c \u1edf t\u00e2m v\u00e0 g\u00f3c n\u1ed9i ti\u1ebfp<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">G\u00f3c \u1edf t\u00e2m l\u00e0 g\u00f3c c\u00f3 \u0111\u1ec9nh tr\u00f9ng v\u1edbi t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n; s\u1ed1 \u0111o g\u00f3c \u1edf t\u00e2m b\u1eb1ng s\u1ed1 \u0111o cung b\u1ecb ch\u1eafn. G\u00f3c n\u1ed9i ti\u1ebfp l\u00e0 g\u00f3c c\u00f3 \u0111\u1ec9nh n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 hai c\u1ea1nh ch\u1ee9a hai d\u00e2y cung; s\u1ed1 \u0111o g\u00f3c n\u1ed9i ti\u1ebfp b\u1eb1ng n\u1eeda s\u1ed1 \u0111o cung b\u1ecb ch\u1eafn. Do \u0111\u00f3, g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n (ch\u1eafn \u0111\u01b0\u1eddng k\u00ednh) lu\u00f4n b\u1eb1ng 90\u00b0.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>T\u00ednh ch\u1ea5t c\u1ee7a ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 nh\u1eefng t\u00ednh ch\u1ea5t quan tr\u1ecdng: ti\u1ebfp tuy\u1ebfn lu\u00f4n vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh t\u1ea1i ti\u1ebfp \u0111i\u1ec3m; t\u1eeb m\u1ed9t \u0111i\u1ec3m n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n k\u1ebb \u0111\u01b0\u1ee3c hai ti\u1ebfp tuy\u1ebfn, v\u00e0 hai ti\u1ebfp tuy\u1ebfn \u0111\u00f3 b\u1eb1ng nhau, \u0111\u1ed3ng th\u1eddi tia n\u1ed1i \u0111i\u1ec3m \u0111\u00f3 v\u1edbi t\u00e2m l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c t\u1ea1o b\u1edfi hai ti\u1ebfp tuy\u1ebfn. Nh\u1eefng t\u00ednh ch\u1ea5t n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh v\u00e0 t\u00ednh to\u00e1n trong c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc v\u1ec1 \u0111\u01b0\u1eddng tr\u00f2n.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">B\u00e0i 1: T\u00ednh chu vi v\u00e0 di\u1ec7n t\u00edch \u0111\u01b0\u1eddng tr\u00f2n b\u00e1n k\u00ednh 7 cm. L\u1eddi gi\u1ea3i: C = 2 \u00d7 3,14 \u00d7 7 = 43,96 cm; S = 3,14 \u00d7 7\u00b2 = 153,86 cm\u00b2.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">B\u00e0i 2: Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m I(1; \u22122), b\u00e1n k\u00ednh 3. L\u1eddi gi\u1ea3i: (x \u2212 1)\u00b2 + (y + 2)\u00b2 = 9.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">B\u00e0i 3: M\u1ed9t g\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn cung 100\u00b0. T\u00ednh s\u1ed1 \u0111o g\u00f3c \u0111\u00f3. L\u1eddi gi\u1ea3i: g\u00f3c n\u1ed9i ti\u1ebfp = 100\u00b0\/2 = 50\u00b0.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">B\u00e0i 4 (tr\u1eafc nghi\u1ec7m): \u0110\u01b0\u1eddng tr\u00f2n x\u00b2 + y\u00b2 = 16 c\u00f3 b\u00e1n k\u00ednh b\u1eb1ng bao nhi\u00eau? A. 16 B. 8 C. 4 D. 2. \u0110\u00e1p \u00e1n: C, v\u00ec R\u00b2 = 16 n\u00ean R = 4.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-568728\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-4.jpg\" alt=\"duong-tron-la-gi-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-tron-la-gi-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2 style=\"text-align: justify;\"><b>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u01b0\u1eddng tr\u00f2n<\/b><\/h2>\n<h3 style=\"text-align: justify;\"><b>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">L\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch m\u1ed9t \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh (t\u00e2m) m\u1ed9t kho\u1ea3ng kh\u00f4ng \u0111\u1ed5i b\u1eb1ng b\u00e1n k\u00ednh R.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>\u0110\u01b0\u1eddng tr\u00f2n kh\u00e1c h\u00ecnh tr\u00f2n th\u1ebf n\u00e0o?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 \u0111\u01b0\u1eddng cong vi\u1ec1n ngo\u00e0i (c\u00f3 chu vi), h\u00ecnh tr\u00f2n l\u00e0 ph\u1ea7n m\u1eb7t ph\u1eb3ng b\u00ean trong (c\u00f3 di\u1ec7n t\u00edch).<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>C\u00f4ng th\u1ee9c chu vi \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Chu vi C = 2\u03c0R = \u03c0d, v\u1edbi R l\u00e0 b\u00e1n k\u00ednh, d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 d\u1ea1ng g\u00ec?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">(x \u2212 a)\u00b2 + (y \u2212 b)\u00b2 = R\u00b2, v\u1edbi t\u00e2m I(a; b) v\u00e0 b\u00e1n k\u00ednh R.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>G\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng bao nhi\u00eau?<\/b><\/h3>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Lu\u00f4n b\u1eb1ng 90\u00b0 (g\u00f3c vu\u00f4ng).<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>K\u1ebft lu\u1eadn<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\"><b>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? <\/b>T\u00f3m l\u1ea1i, \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u t\u00e2m m\u1ed9t kho\u1ea3ng b\u1eb1ng b\u00e1n k\u00ednh, c\u00f3 chu vi C = 2\u03c0R v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh (x \u2212 a)\u00b2 + (y \u2212 b)\u00b2 = R\u00b2. N\u1eafm v\u1eefng c\u00e1c y\u1ebfu t\u1ed1, v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i v\u00e0 g\u00f3c trong \u0111\u01b0\u1eddng tr\u00f2n s\u1ebd gi\u00fap b\u1ea1n h\u1ecdc t\u1ed1t h\u00ecnh h\u1ecdc. \u0110\u1ec3 t\u00ecm hi\u1ec3u th\u00eam, m\u1eddi b\u1ea1n tham kh\u1ea3o c\u00e1c b\u00e0i<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-tron\/\"> <span style=\"font-weight: 400;\">c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n<\/span><\/a><span style=\"font-weight: 400;\">,<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-quat-tron\/\"> <span style=\"font-weight: 400;\">di\u1ec7n t\u00edch h\u00ecnh qu\u1ea1t tr\u00f2n<\/span><\/a><span style=\"font-weight: 400;\"> v\u00e0<\/span><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/1-nam-anh-sang-bang-bao-nhieu-km\/\"> <span style=\"font-weight: 400;\">m\u1ed9t n\u0103m \u00e1nh s\u00e1ng b\u1eb1ng bao nhi\u00eau km<\/span><\/a><span style=\"font-weight: 400;\"> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><b>Xem th\u00eam:<\/b><\/p>\n<ul>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/elip-la-gi\/\">Elip l\u00e0 g\u00ec? Ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc v\u00e0 c\u00e1c y\u1ebfu t\u1ed1<\/a><\/p>\n<\/li>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/bat-phuong-trinh\/\">B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 g\u00ec? C\u00e1ch gi\u1ea3i v\u00e0 v\u00ed d\u1ee5 chi ti\u1ebft<\/a><\/p>\n<\/li>\n<\/ul>\n<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch m\u1ed9t \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh (t\u00e2m) m\u1ed9t kho\u1ea3ng kh\u00f4ng \u0111\u1ed5i b\u1eb1ng b\u00e1n k\u00ednh R.\"}},{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng tr\u00f2n kh\u00e1c h\u00ecnh tr\u00f2n th\u1ebf n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 \u0111\u01b0\u1eddng cong vi\u1ec1n ngo\u00e0i (c\u00f3 chu vi), h\u00ecnh tr\u00f2n l\u00e0 ph\u1ea7n m\u1eb7t ph\u1eb3ng b\u00ean trong (c\u00f3 di\u1ec7n t\u00edch).\"}},{\"@type\":\"Question\",\"name\":\"C\u00f4ng th\u1ee9c chu vi \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Chu vi C = 2\u03c0R = \u03c0d, v\u1edbi R l\u00e0 b\u00e1n k\u00ednh, d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh.\"}},{\"@type\":\"Question\",\"name\":\"Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 d\u1ea1ng g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"(x \u2212 a)\u00b2 + (y \u2212 b)\u00b2 = R\u00b2, v\u1edbi t\u00e2m I(a; b) v\u00e0 b\u00e1n k\u00ednh R.\"}},{\"@type\":\"Question\",\"name\":\"G\u00f3c n\u1ed9i ti\u1ebfp ch\u1eafn n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Lu\u00f4n b\u1eb1ng 90\u00b0 (g\u00f3c vu\u00f4ng).\"}}]}<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? \u0110\u01b0\u1eddng tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh R l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m trong m\u1eb7t ph\u1eb3ng c\u00e1ch \u0111i\u1ec3m O c\u1ed1 \u0111\u1ecbnh m\u1ed9t kho\u1ea3ng kh\u00f4ng \u0111\u1ed5i b\u1eb1ng R. \u0110\u01b0\u1eddng tr\u00f2n l\u00e0 h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n, xu\u1ea5t hi\u1ec7n xuy\u00ean su\u1ed1t ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THCS v\u00e0 THPT. B\u00e0i vi\u1ebft n\u00e0y tr\u00ecnh b\u00e0y \u0111\u01b0\u1eddng [&hellip;]<\/p>\n","protected":false},"author":84,"featured_media":568724,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"\u0111\u01b0\u1eddng tr\u00f2n","_yoast_wpseo_title":"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? Y\u1ebfu t\u1ed1, chu vi v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh","_yoast_wpseo_metadesc":"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? T\u00ecm hi\u1ec3u c\u00e1c y\u1ebfu t\u1ed1, c\u00f4ng th\u1ee9c chu vi C=2\u03c0R, di\u1ec7n t\u00edch S=\u03c0R\u00b2, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.","footnotes":""},"categories":[29235,3910,30453],"tags":[],"class_list":["post-567266","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-goc-to-mo","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? Y\u1ebfu t\u1ed1, chu vi v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh<\/title>\n<meta name=\"description\" content=\"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? T\u00ecm hi\u1ec3u c\u00e1c y\u1ebfu t\u1ed1, c\u00f4ng th\u1ee9c chu vi C=2\u03c0R, di\u1ec7n t\u00edch S=\u03c0R\u00b2, ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-tron-la-gi\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? Y\u1ebfu t\u1ed1, chu vi, di\u1ec7n t\u00edch v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh\" \/>\n<meta property=\"og:description\" content=\"\u0110\u01b0\u1eddng tr\u00f2n l\u00e0 g\u00ec? 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