Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c thu\u1ed9c ch\u01b0\u01a1ng 3 c\u1ee7a to\u00e1n h\u00ecnh h\u1ecdc l\u1edbp 9. \u0110\u00e2y l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c li\u00ean quan t\u1edbi \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng. C\u0169ng nh\u1edd nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng n\u00e0y, c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> c\u00f3 th\u1ec3 gi\u1ea3i b\u00e0i t\u1eadp li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y t\u1eeb d\u1ec5 t\u1edbi kh\u00f3 theo t\u1eebng c\u1ea5p \u0111\u1ed9 su\u1ed1t t\u1edbi t\u1eadn nh\u1eefng b\u00e0i thi trong \u0111\u1ec1 \u0110\u1ea1i h\u1ecdc.<\/p>\n\n\n\n \u0110\u1ec3 gi\u00fap c\u00e1c b\u1ea1n hi\u1ec3u r\u00f5 v\u00e0 n\u1eafm ch\u1eafc ki\u1ebfn th\u1ee9c, Vietlearn s\u1ebd c\u00f9ng b\u1ea1n t\u00ecm hi\u1ec3u t\u1eeb nh\u1eefng y\u1ebfu t\u1ed1 t\u1ea1o th\u00e0nh m\u1ed1i quan h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y. H\u00e3y c\u00f9ng theo d\u00f5i \u1edf b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y nh\u00e9!<\/p>\n\n\n\n \u0110\u1ecbnh ngh\u0129a v\u1ec1 cung v\u00e0 d\u00e2y<\/p>\n\n\n\n Vietlearn s\u1ebd gi\u1edbi thi\u1ec7u cho b\u1ea1n nh\u1eefng \u0111i\u1ec1u c\u01a1 b\u1ea3n, kh\u00e1i ni\u1ec7m v\u1ec1 hai y\u1ebfu t\u1ed1 l\u00e0 cung v\u00e0 d\u00e2y trong \u0111\u01b0\u1eddng tr\u00f2n. C\u00f3 nh\u01b0 v\u1eady, b\u1ea1n s\u1ebd hi\u1ec3u \u0111\u01b0\u1ee3c chi ti\u1ebft b\u00e0i l\u00e0m v\u00e0 \u00e1p d\u1ee5ng cho b\u00e0i t\u1eadp li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y c\u1ee7a b\u1ea1n m\u1ed9t c\u00e1ch t\u1ed1t nh\u1ea5t.<\/p>\n\n\n\n \u0110\u1eb7c \u0111i\u1ec3m v\u1ec1 cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n Cung trong h\u00ecnh h\u1ecdc n\u00f3i chung v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u00f3i ri\u00eang, ch\u00ednh l\u00e0 m\u1ed9t ph\u1ea7n chu vi c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n, kh\u00e9p k\u00edn. Cung tr\u00f2n c\u0169ng c\u00f3 th\u1ec3 hi\u1ec3u l\u00e0 t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n n\u1eb1m gi\u1eefa hai \u0111\u1ea7u m\u00fat \u0111\u00e3 \u0111\u1ecbnh s\u1eb5n. Cung tr\u00f2n c\u00f3 k\u00ed hi\u1ec7u l\u00e0 \u201c\u2312\u201d.<\/p>\n\n\n\n Cung trong \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n C\u00e1c t\u00ednh cung c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 \u0111o g\u00f3c t\u1ea1o b\u1edfi hai \u0111o\u1ea1n th\u1eb3ng r\u1ed3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c v\u1edbi L l\u00e0 chi\u1ec1u d\u00e0i cung tr\u00f2n:<\/p>\n\n\n\n \u0110\u1eb7c \u0111i\u1ec3m v\u1ec1 d\u00e2y cung c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n D\u00e2y hay c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 d\u00e2y cung c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ch\u00ednh l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng n\u00f3i t\u1eeb hai \u0111\u1ea7u \u0111i\u1ec3m thu\u1ed9c tr\u00ean c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. D\u00e2y cung c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u00e1t tuy\u1ebfn.<\/p>\n\n\n\n D\u00e2y cung AB trong \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O<\/p>\n\n\n\n D\u00e2y cung c\u0169ng c\u00f3 c\u00e1c t\u00ednh ch\u1ea5t ri\u00eang nh\u01b0 c\u00e1c \u0111\u01b0\u1eddng \u0111\u1eb7c bi\u1ec7t trong tam gi\u00e1c:<\/p>\n\n\n\n Hai d\u00e2y cung n\u1eb1m trong c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1ch \u0111\u1ec1u t\u00e2m khi v\u00e0 ch\u1ec9 khi ch\u1ee9ng c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau.<\/p>\n\n\n\n \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t d\u00e2y cung \u0111\u1ec1u \u0111i qua t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n Hai \u0111\u01b0\u1eddng c\u00e1t tuy\u1ebfn c\u1ee7a hai d\u00e2y cung c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m th\u00ec c\u00f3 t\u00ednh ch\u1ea5t ph\u01b0\u01a1ng t\u00edch c\u1ee7a m\u1ed9t \u0111i\u1ec3m.<\/p>\n\n\n\n Hai g\u00f3c thu\u1ed9c c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau khi hai d\u00e2y cung ch\u1eafn n\u00f3 b\u1eb1ng nhau ho\u1eb7c c\u00f9ng \u0111\u01b0\u1ee3c ch\u1eafn b\u1edfi m\u1ed9t d\u00e2y cung.<\/p>\n\n\n\n V\u1edbi nh\u1eefng ki\u1ebfn th\u1ee9c tr\u00ean, b\u1ea1n c\u00f3 th\u1ec3 \u0111i b\u00e0i to\u00e1n 9 li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng h\u01a1n ngay d\u01b0\u1edbi \u0111\u00e2y c\u00f9ng Vietlearn.<\/p>\n\n\n\n L\u00fd thuy\u1ebft t\u1ed5ng qu\u00e1t v\u1ec1 m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y<\/p>\n\n\n\n Gi\u1ea3 s\u1eed, x\u00e9t tr\u01b0\u1eddng h\u1ee3p \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1ee3c cho l\u00e0 c\u00e1c \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 \u0111\u1ed9 l\u1edbn nh\u01b0 nhau ho\u1eb7c c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n. Ta c\u00f3 th\u1ec3 c\u00f3 hai \u0111\u1ecbnh l\u00fd v\u1ec1 to\u00e1n 9 li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y nh\u01b0 sau:<\/p>\n\n\n\n M\u1ed1i li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 cung<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 1 v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y<\/p>\n\n\n\n S\u1ed1 \u0111o c\u1ee7a hai cung tr\u00f2n b\u1eb1ng nhau th\u00ec hai d\u00e2y cung c\u1ee7a hai cung tr\u00f2n c\u0169ng c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau<\/p>\n\n\n\n cung MN = cung PQ=> MN= PQ<\/p>\n\n\n\n Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu hai d\u00e2y cung c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau th\u00ec c\u00e1c cung \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh c\u0169ng b\u1eb1ng nhau<\/p>\n\n\n\n cung MN = cung PQ => MN= PQ<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 2 v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y<\/p>\n\n\n\n Cung tr\u00f2n c\u00f3 \u0111\u1ed9 l\u1edbn l\u1edbn h\u01a1n cung tr\u00f2n c\u00f2n l\u1ea1i th\u00ec s\u1ebd c\u0103ng \u0111\u01b0\u1ee3c m\u1ed9t d\u00e2y cung l\u1edbn h\u01a1n d\u00e2y cung \u0111\u01b0\u1ee3c c\u0103ng b\u1edfi cung tr\u00f2n nh\u1ecf h\u01a1n.<\/p>\n\n\n\n cung MN > cung PQ=> MN > PQ<\/p>\n\n\n\n Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu cung tr\u00f2n c\u00f3 \u0111\u1ed9 l\u1edbn nh\u1ecf h\u01a1n cung tr\u00f2n c\u00f2n l\u1ea1i th\u00ec s\u1ebd c\u0103ng \u0111\u01b0\u1ee3c m\u1ed9t d\u00e2y cung ng\u1eafn h\u01a1n d\u00e2y cung \u0111\u01b0\u1ee3c c\u0103ng b\u1edfi cung tr\u00f2n nh\u1ecf h\u01a1n.<\/p>\n\n\n\n cung MN < cung PQ=> MN < PQ<\/p>\n\n\n\n C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m m\u00e0 h\u1ecdc sinh<\/a> n\u00ean l\u01b0u \u00fd v\u1ec1 m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y<\/p>\n\n\n\n Trong c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n x\u00e1c \u0111\u1ecbnh, hai cung \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi hai d\u00e2y cung ch\u1eafn song song v\u1edbi nhau th\u00ec c\u00f3 \u0111\u1ed9 l\u1edbn b\u1eb1ng nhau.<\/p>\n\n\n\n Trong c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua \u0111i\u1ec3m ch\u00ednh gi\u1eefa m\u1ed9t cung tr\u00f2n th\u00ec s\u1ebd \u0111i qua trung \u0111i\u1ec3m c\u1ee7a d\u00e2y cung ch\u1eafn cung tr\u00f2n \u0111\u00f3<\/p>\n\n\n\n Trong c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, \u0111\u01b0\u1eddng k\u00ednh \u0111i qua trung \u0111i\u1ec3m c\u1ee7a d\u00e2y cung kh\u00f4ng \u0111i qua t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n th\u00ec s\u1ebd \u0111i qua \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ee7a cung \u0111\u01b0\u1ee3c t\u1ea1o ra b\u1edfi d\u00e2y cung \u0111\u00f3.<\/p>\n\n\n\n Trong c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, n\u1ebfu b\u00e1n k\u00ednh vu\u00f4ng g\u00f3c v\u1edbi d\u00e2y cung th\u00ec n\u00f3 \u0111i qua \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ee7a cung \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh.<\/p>\n\n\n\n B\u00e0i t\u1eadp v\u1ec1 so s\u00e1nh d\u00e2y cung v\u00e0 cung tr\u00f2n<\/p>\n\n\n\n \u0110\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i t\u1eadp n\u00e0y m\u1ed9t c\u00e1ch nhanh ch\u00f3ng, Vietlearn chia s\u1ebb v\u1edbi b\u1ea1n ph\u01b0\u01a1ng ph\u00e1p d\u1ef1a tr\u00ean nh\u1eefng \u0111\u1ecbnh l\u00fd \u0111\u00e3 n\u00eau tr\u00ean:<\/p>\n\n\n\n Hai cung tr\u00f2n c\u00f3 \u0111\u1ed9 l\u1edbn b\u1eb1ng nhau khi hai d\u00e2y cung ch\u1eafn n\u00f3 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau<\/p>\n\n\n\n Hai d\u00e2y cung c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau khi hai cung tr\u00f2n b\u1ecb ch\u1eafn c\u00f3 \u0111\u1ed9 l\u1edbn b\u1eb1ng nhau<\/p>\n\n\n\n Cung tr\u00f2n n\u00e0o l\u1edbn h\u01a1n s\u1ebd c\u00f3 d\u00e2y cung l\u1edbn h\u01a1n v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n\n\n\n D\u00e2y cung tr\u00f2n n\u00e0o c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn h\u01a1n th\u00ec s\u1ebd c\u00f3 cung tr\u00f2n l\u1edbn h\u01a1n v\u00e0 ng\u01b0\u1ee3c l\u1ea1i<\/p>\n\n\n\n B\u00e0i t\u1eadp minh h\u1ecda<\/p>\n\n\n\n Sau khi so s\u00e1nh \u0111\u01b0\u1ee3c c\u00e1c d\u00e2y cung v\u00e0 cung tr\u00f2n, m\u1ed9t s\u1ed1 b\u00e0i s\u1ebd b\u1eaft t\u00ednh to\u00e1n \u0111\u1ea1i l\u01b0\u1ee3ng c\u1ee5 th\u1ec3 ho\u1eb7c c\u00f3 th\u1ec3 l\u00e0 ch\u1ee9ng minh c\u00e1c \u0111\u1ecbnh th\u1ee9c theo y\u00eau c\u1ea7u. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 d\u1ef1a v\u00e0o ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc k\u1ebft h\u1ee3p v\u1edbi c\u00e1c \u0111\u1ecbnh l\u00fd c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n, h\u00ecnh tam gi\u00e1c \u0111\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n.<\/p>\n\n\n\n Mong r\u1eb1ng b\u00e0i vi\u1ebft tr\u00ean, Vietlearn \u0111\u00e3 gi\u00fap c\u00e1c b\u1ea1n ph\u1ea7n n\u00e0o hi\u1ec3u \u0111\u01b0\u1ee3c m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y. T\u1eeb \u0111\u00f3 gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c b\u00e0i to\u00e1n trong gi\u00e1o tr\u00ecnh to\u00e1n h\u1ecdc l\u1edbp 9 v\u00e0 c\u1ea3 ch\u1eb7ng \u0111\u01b0\u1eddng h\u1ecdc t\u1eadp<\/a> sau n\u00e0y. Ch\u00fac b\u1ea1n th\u00e0nh c\u00f4ng!<\/p>\n\n\n\n <\/p>\n\n\n\n G\u00f3c \u1edf t\u00e2m s\u1ed1 \u0111o cung<\/p>\n\n\n\n G\u00f3c n\u1ed9i ti\u1ebfp<\/p>\n\n\n\n V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n \u2013 H\u1ecdc h\u00ecnh to\u00e1n 9<\/p>\n\n\n\n V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n \u2013 L\u00fd thuy\u1ebft v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i<\/p>\n\n\n\n \u0110\u01b0\u1eddng<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Li\u00ean h\u1ec7 gi\u1eefa cung v\u00e0 d\u00e2y l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c thu\u1ed9c ch\u01b0\u01a1ng 3 c\u1ee7a to\u00e1n h\u00ecnh h\u1ecdc l\u1edbp 9. \u0110\u00e2y l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c li\u00ean quan t\u1edbi \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng. C\u0169ng nh\u1edd nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng n\u00e0y, c\u00e1c b\u1ea1n h\u1ecdc sinh c\u00f3 th\u1ec3 gi\u1ea3i b\u00e0i t\u1eadp […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-1123","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=1123"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1123\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}