H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-19T03:53:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-163.png\" \/>\n\t<meta property=\"og:image:width\" content=\"206\" \/>\n\t<meta property=\"og:image:height\" content=\"189\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"H\u00e0 Trang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"H\u00e0 Trang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\",\"url\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\",\"name\":\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\",\"isPartOf\":{\"@id\":\"https:\/\/lop12.edu.vn\/#website\"},\"datePublished\":\"2018-03-19T03:53:52+00:00\",\"dateModified\":\"2018-03-19T03:53:52+00:00\",\"author\":{\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\"},\"breadcrumb\":{\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/lop12.edu.vn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 2 – B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/lop12.edu.vn\/#website\",\"url\":\"https:\/\/lop12.edu.vn\/\",\"name\":\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/lop12.edu.vn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\",\"name\":\"H\u00e0 Trang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"caption\":\"H\u00e0 Trang\"},\"url\":\"https:\/\/lop12.edu.vn\/author\/trangvth2\/\"}]}<\/script>\n","yoast_head_json":{"title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","og_locale":"en_US","og_type":"article","og_title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","og_description":"B\u00e0i 1 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, […]","og_url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","og_site_name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam","article_published_time":"2018-03-19T03:53:52+00:00","og_image":[{"width":206,"height":189,"url":"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-163.png","type":"image\/png"}],"author":"H\u00e0 Trang","twitter_card":"summary_large_image","twitter_misc":{"Written by":"H\u00e0 Trang","Est. reading time":"12 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","name":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","isPartOf":{"@id":"https:\/\/lop12.edu.vn\/#website"},"datePublished":"2018-03-19T03:53:52+00:00","dateModified":"2018-03-19T03:53:52+00:00","author":{"@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45"},"breadcrumb":{"@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/lop12.edu.vn\/"},{"@type":"ListItem","position":2,"name":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 2 – B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u"}]},{"@type":"WebSite","@id":"https:\/\/lop12.edu.vn\/#website","url":"https:\/\/lop12.edu.vn\/","name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/lop12.edu.vn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45","name":"H\u00e0 Trang","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","caption":"H\u00e0 Trang"},"url":"https:\/\/lop12.edu.vn\/author\/trangvth2\/"}]}},"_links":{"self":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311"}],"collection":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/comments?post=22311"}],"version-history":[{"count":1,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311\/revisions"}],"predecessor-version":[{"id":22330,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311\/revisions\/22330"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media\/22312"}],"wp:attachment":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media?parent=22311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/categories?post=22311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/tags?post=22311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, CD = c.<\/p>\n

Theo t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c vu\u00f4ng \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n: BO = CO = 1\/2 AD. Suy ra A, B, C, D n\u1eb1m tr\u00ean m\u1eb7t c\u1ea7u t\u00e2m O,<\/p>\n

T\u00e2m m\u1eb7t c\u1ea7u O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AD<\/p>\n

a) T\u00ecm t\u1eadp h\u1ee3p c\u00e1c m\u1eb7t c\u1ea7u \u0111i qua hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t A, B cho tr\u01b0\u1edbc.<\/p>\n

b) T\u00ecm t\u1eadp h\u1ee3p tam c\u00e1c m\u1eb7t c\u1ea7u \u0111i qua \u0111\u01b0\u1eddng tr\u00f2n cho tr\u01b0\u1edbc.<\/p>\n

c) C\u00f3 hay kh\u00f4ng m\u1ed9t m\u1eb7t c\u1ea7u \u0111i qua m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m ng\u00f2i m\u1eb7t ph\u1eb3ng c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n

a) G\u1ecdi I l\u00e0 tam m\u1eb7t c\u1ea7u \u0111i qua \u0111i\u1ec3m A, B cho tr\u01b0\u1edbc, khi \u0111\u00f3 IA = IB. v\u1eady I n\u1eb1m tr\u00ean m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a AB.<\/p>\n

b) I l\u00e0 t\u00e2m m\u1eb7t m\u1ea7u \u0111i qua ba \u0111i\u1ec3m A, B, C cho tr\u01b0\u1edbc v\u00e0 khi v\u00e0 ch\u1ec9 kh\u1ec9 IA = IB = IC. V\u1eady:<\/p>\n

+ N\u1ebfu ba \u0111i\u1ec3m A, B, C kh\u00f4ng th\u1eb3ng h\u00e0ng th\u00ec t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m I l\u00e0 trung tr\u1ef1c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i tuy\u1ebfn tam gi\u00e1c ABC.<\/p>\n

+ n\u1ebfu ba \u0111i\u1ec3m A, B, C th\u0103ng h\u00e0ng v\u00e0 \u0111\u00f4i m\u1ed9t ph\u00e2n bi\u1ec7t th\u00ec t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m I l\u00e0 tr\u1ee5c tr\u1ef1c c\u1ee7a c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n

c) I l\u00e0 t\u00e2m m\u1eb7t c\u1ea7u \u0111i qua \u0111\u01b0\u1eddng tr\u00f2n (C) cho tr\u01b0\u1edbc khi v\u00e0 ch\u1ec9 khi I c\u00e1ch \u0111\u1ec1u m\u1ecdi \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n. V\u1eady t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m I l\u00e0 trung tr\u1ef1c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n (C )<\/p>\n

d) G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m n\u1eb1m ngo\u00e0i m\u1eb7t ph\u1eb3ng c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n C. l\u1ea5y \u0111i\u1ec3m A n\u1eb1m tr\u00ean (C) v\u00e0 g\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a trung tr\u1ef1c \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a MA. Khi \u0111\u00f3 m\u1eb7t c\u1ea7u t\u00e2m I, b\u00e1n k\u00ednh R = IA = IM l\u00e0 m\u1eb7t c\u1ea7u t\u00e2m I, b\u00e1n k\u00ednh R = IA = IM l\u00e0 m\u1eb7t c\u1ea7u \u0111i qua \u0111\u01b0\u1eddng tr\u00f2n C v\u00e0 \u0111i qua \u0111i\u1ec3m M.<\/p>\n

Cho \u0111i\u1ec3m M n\u1eb1m trong m\u1eb7t c\u1ea7u (S). Trong c\u00e1c m\u1ec7nh \u0111\u1ec1 sau m\u1ec7nh \u0111\u1ec1 n\u00e0o \u0111\u00fang?<\/p>\n

a) M\u1ecdi m\u1eb7t ph\u1eb3ng \u0111i qua M \u0111\u1ec1u c\u1eaft (S) theo m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n

b) M\u1ecdi \u0111\u01b0\u1eddng th\u1eb3ng qua M \u0111\u1ec1u c\u1eaft (S) t\u1ea1i hai \u0111i\u1ec3m ph\u00e2n bi\u1ec7t.<\/p>\n

<\/div>\n
C\u1ea3 a, b \u0111\u1ec1u \u0111\u00fang.<\/p>\n
\n
\n
B\u00e0i 4 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
Cho \u0111\u01b0\u1eddng th\u1eb3ng d v\u00e0 \u0111i\u1ec3m A kh\u00f4ng n\u1eb1m tr\u00ean d. x\u00e9t c\u00e1c m\u1eb7t c\u1ea7u \u0111i qua A v\u00e0 c\u00f3 t\u00e2m n\u1eb1m tr\u00ean d, ch\u1ee9ng minh r\u1eb1ng c\u00e1c m\u1eb7t c\u1ea7u \u0111\u00f3 lu\u00f4n lu\u00f4n \u0111i qua m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u1ed1 \u0111\u1ecbnh.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
$\"\"$ <\/div>\n
G\u1ecdi S l\u00e0 m\u1eb7t c\u1ea7u \u0111i qua \u0111i\u1ec3m A c\u00f3 t\u00e2m O n\u1eb1m tr\u00ean d (h\u00ecnh v\u1ebd b\u00ean). G\u1ecdi (P) l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua A v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi d. khi \u0111\u00f3 (P) c\u1eaft m\u1eb7t c\u1ea7u (S) theo giao tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n (C), c\u00f3 t\u00e2m I l\u00e0 giao c\u1ee7a m\u1eb7t ph\u1eb3ng (P) v\u1edbi d, b\u00e1n k\u00ednh r = IA => (C) c\u1ed1 \u0111\u1ecbnh.<\/p>\n
B\u00e0i 5 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
Cho m\u1eb7t c\u1ea7u c\u1ed1 \u0111\u1ecbnh (C).<\/p>\n
M\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang?<\/p>\n
a) M\u1ecdi m\u1eb7t c\u1ee7a n\u00f3 l\u00e0 \u0111a gi\u00e1c n\u00ean m\u1eb7t c\u1ea7u th\u00ec m\u1ecdi m\u1eb7t c\u1ee7a n\u00f3 l\u00e0 \u0111a gi\u00e1c n\u1ed9i.<\/p>\n
b) \u0110\u01b0\u1eddng tr\u00f2n th\u00ec \u0111a di\u1ec7n \u0111\u00f3 n\u1ed9i ti\u1ebfn n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng trong th\u00ec \u0111a di\u1ec7n \u0111\u00f3 n\u1ed9i ti\u1ebfp.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
<\/div>\n
$\"\"$ <\/p>\n
ABCD n\u1ed9i ti\u1ebfp t\u1ea1i \u0111i\u1ec3m E n\u1eb1m trong m\u1eb7t ph\u1eb3ng (BCD). C\u00f3 6 m\u1eb7t ABC, c\u00e1c m\u1eb7t \u0111\u1ec1u l\u00e0 h\u00ecnh \u0111a di\u1ec7n c\u1ea7u. v\u00ec n\u1ebfu c\u00f3 C, D, E th\u00ec n\u00f3 l\u00e0 h\u00ecnh c\u1ea5u \u0111\u00f3 ch\u00ednh l\u00e0 ti\u1ebfp di\u1ec7n tr\u00ean S.<\/p>\n
B\u00e0i 7 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
a) T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u ngo\u00e0i ti\u1ebfp h\u00ecnh b\u1eb1ng a v\u00e0 chi\u1ec1u cao h.<\/p>\n
b) Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 . G\u1ecdi A\u2019, B\u2019, C\u2019 D\u2019 l\u1ea7n l\u01b0\u1ee3t l\u00e0 csac trung \u0111i\u1ec3m c\u1ee7a A, B, C, D. t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u \u0111\u00f3.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
a) Gi\u1ea3 s\u1eed SH l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u S.ABC. khi \u0111\u00f3 SA SB = SC n\u00ean m\u1ecdi \u0111i\u1ec3m n\u1eb1m tr\u00ean SH c\u00e1ch \u0111\u1ec1u A, B, C.<\/p>\n
Trong m\u1eb7t ph\u1eb3ng (SAH) \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a SA c\u1eaft SH t\u1ea1i O l\u00e0 t\u00e2m m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp h\u00ecnh ch\u00f3p, b\u00e1n k\u00ednh c\u1ea7u l\u00e0 R = SO.<\/p>\n
G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m SA th\u00ec t\u1ee9 gi\u00e1c AHOI n\u1ed9i ti\u1ebfp.<\/p>\n
$\"\"$ <\/p>\n
b)G\u1ecdi SH l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u SABCD th\u00ec H l\u00e0 t\u00e2m h\u00ecnh vu\u00f4ng ABCD v\u00e0 SH \u0111i qua t\u00e2m H\u2019 c\u1ee7a h\u00ecnh vu\u00f4ng A\u2019B\u2019C\u2019D\u2019. h\u00ecnh v\u1ebd. M\u1ecdi \u0111i\u1ec3m n\u1eb1m tr\u00ean SH v\u00e0 c\u00e1ch \u0111\u1ec1u 4 \u0111i\u1ec3m A, B, C, D v\u00e0 c\u0169ng l\u00e0 c\u00e1ch \u0111\u1ec1u 4 \u0111i\u1ec3m A\u2019, B\u2019, C\u2019, D\u2019. tr\u00ean SH x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m O sao cho OA = OA\u2019 th\u00ec O c\u00e1c ddefu 8 \u0111\u1ec9nh A, B, C, D, A\u2019, B\u2019, C\u2019, D\u2019 t\u1ee9c 8 \u0111\u1ec9nh \u0111\u00f3 n\u1eb1m tr\u00ean m\u1eb7t c\u1ea7u t\u00e2m O, b\u00e1n k\u00ednh R = OA. \u0110i\u1ec3m O l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u01a1ng th\u1eb3ng SH v\u00e0 m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n AA\u2019.<\/p>\n
Do \u0394SAC c\u00e2n t\u1ea1i S. G\u1ecdi I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AA\u2019 th\u00ec \u0394SIO c\u0169ng vu\u00f4ng c\u00e2n t\u1ea1i I n\u00ean IO = SI = 3a\/4. Suy ra:<\/p>\n
$\"\"$ <\/p>\n
Th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u l\u00e0:<\/p>\n
$\"\"$ <\/p>\n
B\u00e0i 8 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
Cho t\u1ee9 di\u1ec7n ABCD, v\u1edbi AB= CD = c, AC = BD = b, AD = BC = a.<\/p>\n
a) T\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp t\u1ee9 di\u1ec7n.<\/p>\n
b) Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1ed9t m\u1eb7t c\u1ea7u ti\u1ebfp x\u1ee9c v\u1edbi b\u1ed1n m\u1eb7t c\u1ea7u t\u01b0 di\u1ec7n (n\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1eb7t c\u1ea7u n\u1ed9i ti\u1ebfp t\u1ee9 di\u1ec7n).<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
<\/div>\n
$\"\"$ <\/p>\n
a) G\u1ecdi I, J l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 CD th\u00ec IJ \u22a5 AB, IJ \u22a5 Cd<\/p>\n
G\u1ecdi O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a IJ th\u00ec OA = OB v\u00e0 OC = OD.<\/p>\n
Do AB = CD = c n\u00ean hai tam gi\u00e1c vu\u00f4ng OIB v\u00e0 OJC b\u1eb1ng nahu n\u00ean OB = Oc.<\/p>\n
V\u1eady O c\u00e1ch \u0111\u1ec1u 4 \u0111\u1ec9nh A, B, C, D<\/p>\n
M\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp t\u1ee9 di\u1ec7n ABCD c\u00f3 t\u00e2m O, b\u00e1n k\u00ednh R = OA.<\/p>\n
Ta c\u00f3:<\/p>\n
$\"\"$ <\/p>\n
V\u00ec CI l\u00e0 trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c ABC n\u00ean.<\/p>\n
$\"\"$ <\/p>\n
di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp t\u1ee9 di\u1ec7n ABCD l\u00e0<\/p>\n
$\"\"$ <\/p>\n
b) C\u00e1c m\u1eb7t c\u1ee7a t\u1ee9 di\u1ec7n l\u00e0 tam gi\u00e1c b\u1eb1ng nhau (\u0111\u1ec1u c\u00f3 ba c\u1ea1nh l\u00e0 a, b, c) n\u00ean c\u00e1c \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u00e1c tam gi\u00e1c \u0111\u00f3 c\u00f3 b\u00e1n k\u00ednh r b\u1eb1ng nhau. C\u00e1c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 \u0111\u1ec1u n\u1eb1m tr\u00ean m\u1eb7t c\u1ea7u (O, R) n\u00ean kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m O t\u1edbi c\u00e1c m\u1eb7t ph\u1eb3ng ch\u1ee9a c\u00e1c \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 b\u1eb1ng nhau v\u00e0 b\u1eb1ng<\/p>\n
$\"\"$ <\/p>\n
V\u1eady m\u1eb7t c\u1ea7u t\u00e2m O b\u00e1n k\u00ednh h l\u00e0 m\u1eb7t c\u1ea7u n\u1ed9i ti\u1ebfp t\u1ee9 di\u1ec7n ABCD.<\/p>\n
B\u00e0i 9 (trang 46 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
T\u00ecm di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp h\u00ecnh ch\u00f3p SABC bi\u1ebft SA = a, SB = b, SC = c v\u00e0 ba c\u1ea1nh Sa, SB, SC \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c. Ch\u1ee9ng minh r\u1eb1ng c\u00e1c \u0111i\u1ec3m S, G, I th\u1eb3ng h\u00e0ng, trong \u0111\u00f3 G l\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC v\u00e0 I l\u00e0 t\u00e2m m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp h\u00ecnh ch\u00f3p S.ABC.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
<\/div>\n
$\"\"$ <\/p>\n
G\u1ecdi J l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB. V\u00ec tam gi\u00e1c SAB vu\u00f4ng \u1edf \u0111\u1ec9nh S n\u00ean \u00cd = JA = IB (h\u00ecnh v\u1ebd b\u00ean)<\/p>\n
G\u1ecdi \u0394 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (SAB) t\u1ea1i J th\u00ec m\u1ecdi \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng \u0394 \u0111\u1ec1u c\u00e1ch 3 \u0111i\u1ec3m S, A, B. B\u1edfi v\u1eady n\u1ebfu g\u1ecdi I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0394 v\u1edbi m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n SC th\u00ec I c\u00e1c \u0111\u1ec1u 4 \u0111i\u1ec3m S, A, B, C.<\/p>\n
V\u1eady m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp h\u00ecnh ch\u00f3p c\u00f3 t\u00e2m I, b\u00e1n k\u00ednh R = IA.<\/p>\n
$\"\"$ <\/p>\n
Di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u b\u1eb1ng: S = 4\u03c0R^{2<\/sup>=\u03c0(a^{2<\/sup>+b^{2<\/sup>\u00a0+ c^{2<\/sup>)<\/p>\n}}}}
V\u00ec (SC \/\/ IJ n\u00ean SI c\u1eaft CJ t\u1ea1i \u0111i\u1ec3m G v\u00e0 do SC = 2IJ n\u00ean CG = 2GJ. Do CJ l\u00e0 trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c ABC n\u00ean G l\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC.<\/p>\n
B\u00e0i 10 (trang 46 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n
a) Ch\u1ee9ng minh r\u1eb1ng m\u1ed9t h\u00ecnh l\u0103ng tr\u1ee5 c\u00f3 m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp khi v\u00e0 ch\u1ec9 khi n\u00f3 l\u00e0 h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng v\u00e0 \u0111\u00e1y l\u00e0 \u0111a gi\u00e1c n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n
b) Trong c\u00e1c h\u00ecnh h\u1ed9p n\u1ed9i ti\u1ebfp m\u1eb7t c\u1ea7u cho tr\u01b0\u1edbc, h\u00ecnh h\u1ed9p n\u00e0o c\u00f3 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n l\u1edbn nh\u1ea5t.<\/p>\n
L\u1eddi gi\u1ea3i:<\/b><\/p>\n
<\/div>\n
$\"\"$ <\/p>\n
a) N\u1ebfu H l\u00e0 h\u00ecnh l\u0103ng tr\u1ee5 c\u00f3 m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp th\u00ec c\u00e1c m\u1eb7t b\u00ean l\u00e0 nh\u1eefng h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp nen ph\u1ea3i l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt. ngo\u00e0i ra H c\u00f3 m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp n\u00ean m\u1eb7t \u0111\u00e1y ph\u1ea3i l\u00e0 \u0111a gi\u00e1c c\u00f3 \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp.<\/p>\n
Ng\u01b0\u1ee3c l\u1ea1i cho H l\u00e0 l\u0103ng tr\u1ee5 \u0111\u00fang c\u00f3 c\u00e1c \u0111\u01b0\u1eddng tr\u00f2n C v\u00e0 C\u2019 ngo\u1ea1i ti\u1ebfp c\u00e1c \u0111a gi\u00e1c (h\u00ecnh v\u1ebd).<\/p>\n
G\u1ecdi I, I\u2019 l\u00e0 t\u00e2m c\u1ee7a C v\u00e0 C\u2019 th\u00ec II\u2019 l\u00e0 tr\u1ee5c c\u1ee7a c\u1ea3 hai \u0111\u01b0\u1eddng tr\u00f2n, g\u1ecdi O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a II\u2019 th\u00ec c\u00e1ch \u0111\u1ec1u t\u1ea5u c\u1ea3 c\u00e1c \u0111\u1ec9nh c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111a cho.<\/p>\n
V\u1eady h\u00ecnh l\u0103ng tr\u1ee5 \u1ea5y c\u00f3 m\u1eb7t c\u1ea7u ngo\u1ea1i ti\u1ebfp.<\/p>\n
b) N\u1ebfu h\u00ecnh h\u1ed9p H n\u1ed9i ti\u1ebfp m\u1eb7t c\u1ea7u S(O, R) th\u00ec c\u00e1c m\u1eb7t c\u1ee7a H ph\u1ea3i l\u00e0 nh\u1eefng h\u00ecnh ch\u1eef nh\u1eadt, v\u1eady H l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt m\u00e0 O l\u00e0 c\u00e1c giao \u0111i\u1ec3m c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o, v\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o d = 2R.<\/p>\n
G\u1ecdi a, b, c l\u00e0 c\u00e1c k\u00edch th\u01b0\u1edbc c\u1ee7a h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt \u0111\u00f3 th\u00ec a^{2<\/sup>+b^{2<\/sup>+c^{2<\/sup>=d^{2<\/sup>=4R^{2<\/sup>. G\u1ecdi S l\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh h\u1ed9p th\u00ec ta c\u00f3:<\/p>\n}}}}}
S = 2ab +2bc + 2ac \u22642(a^{2<\/sup>+b^{2<\/sup>+c^{2<\/sup>\u00a0)=8R^{2<\/sup>.<\/p>\n}}}}
V\u1eady S \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng 8R^{2<\/sup>\u00a0th\u00ec<\/p>\n}
$\"\"$ <\/p>\n
t\u1ee9c l\u00e0 H l\u00e0 h\u00ecnh l\u1eadp ph\u01b0\u01a1ng.<\/p>\n
<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
B\u00e0i 1 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, […]<\/p>\n","protected":false},"author":3,"featured_media":22312,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\nH\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-19T03:53:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-163.png\" \/>\n\t<meta property=\"og:image:width\" content=\"206\" \/>\n\t<meta property=\"og:image:height\" content=\"189\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"H\u00e0 Trang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"H\u00e0 Trang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\",\"url\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\",\"name\":\"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\",\"isPartOf\":{\"@id\":\"https:\/\/lop12.edu.vn\/#website\"},\"datePublished\":\"2018-03-19T03:53:52+00:00\",\"dateModified\":\"2018-03-19T03:53:52+00:00\",\"author\":{\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\"},\"breadcrumb\":{\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/lop12.edu.vn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 2 – B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/lop12.edu.vn\/#website\",\"url\":\"https:\/\/lop12.edu.vn\/\",\"name\":\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/lop12.edu.vn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45\",\"name\":\"H\u00e0 Trang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g\",\"caption\":\"H\u00e0 Trang\"},\"url\":\"https:\/\/lop12.edu.vn\/author\/trangvth2\/\"}]}<\/script>\n","yoast_head_json":{"title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","og_locale":"en_US","og_type":"article","og_title":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","og_description":"B\u00e0i 1 (trang 45 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Trong kh\u00f4ng gian cho ba \u0111o\u1ea1n th\u1eb3ng AB, BC, CD sao cho AB \u22a5 BC, BC \u22a5 CD, CD\u22a5AB. Ch\u1ee9ng minh r\u1eb1ng c\u00f3 m\u1eb7t c\u1ea7u \u0111i qua b\u1ed1n \u0111i\u1ec3m A, B, C, D. t\u00ednh b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u n\u1ebfu AB = a, BC = b, […]","og_url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","og_site_name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam","article_published_time":"2018-03-19T03:53:52+00:00","og_image":[{"width":206,"height":189,"url":"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-163.png","type":"image\/png"}],"author":"H\u00e0 Trang","twitter_card":"summary_large_image","twitter_misc":{"Written by":"H\u00e0 Trang","Est. reading time":"12 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","url":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/","name":"H\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u","isPartOf":{"@id":"https:\/\/lop12.edu.vn\/#website"},"datePublished":"2018-03-19T03:53:52+00:00","dateModified":"2018-03-19T03:53:52+00:00","author":{"@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45"},"breadcrumb":{"@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-1-mat-cau-khoi-cau\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/lop12.edu.vn\/"},{"@type":"ListItem","position":2,"name":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 2 – B\u00e0i 1: M\u1eb7t c\u1ea7u, kh\u1ed1i c\u1ea7u"}]},{"@type":"WebSite","@id":"https:\/\/lop12.edu.vn\/#website","url":"https:\/\/lop12.edu.vn\/","name":"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/lop12.edu.vn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/2da855e5d06b553ac0065157cc261a45","name":"H\u00e0 Trang","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/lop12.edu.vn\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/545a8100db1147f314111301d261dc33?s=96&d=mm&r=g","caption":"H\u00e0 Trang"},"url":"https:\/\/lop12.edu.vn\/author\/trangvth2\/"}]}},"_links":{"self":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311"}],"collection":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/comments?post=22311"}],"version-history":[{"count":1,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311\/revisions"}],"predecessor-version":[{"id":22330,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/posts\/22311\/revisions\/22330"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media\/22312"}],"wp:attachment":[{"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/media?parent=22311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/categories?post=22311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lop12.edu.vn\/wp-json\/wp\/v2\/tags?post=22311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}