B\u00e0i 4 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0T\u00ecm t\u1eadp h\u1ee3p t\u00e2m c\u00e1c m\u1eb7t c\u1ea7u lu\u00f4n c\u00f9ng ti\u1ebfp x\u00fac v\u1edbi ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c cho tr\u01b0\u1edbc.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-4-trang-49-sgk-hinh-hoc-12.png\")
<\/p>\n
*X\u00e9t m\u1eb7t c\u1ea7u (S) c\u00f3 t\u00e2m O, b\u00e1n k\u00ednh R v\u00e0 ti\u1ebfp x\u00fac v\u1edbi ba c\u1ea1nh BC, CA, AB c\u1ee7a tam gi\u00e1c ABC t\u1ea1i M, N, P. H l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a O tr\u00ean mp(ABC), ta c\u00f3:<\/p>\n
OM \u22a5 AB => BM \u22a5 AB<\/p>\n
(theo \u0111\u1ecbnh l\u00ed ba \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c)<\/p>\n
T\u01b0\u01a1ng t\u1ef1: HN \u22a5 BC, HP \u22a5 AC<\/p>\n
Ta c\u00f3: OM = ON = OP = R<\/p>\n
Khi \u0111\u00f3 \u0394OHM = \u0394OHN = \u0394OHP<\/p>\n
Suy ra HM = HN = HP<\/p>\n
Ch\u1ee9ng t\u1ecf H l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n
V\u1eady t\u00e2m O c\u1ee7a m\u1eb7t c\u1ea7u thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng d vu\u00f4ng g\u00f3c v\u1edbi mp(ABC) t\u1ea1i t\u00e2m H c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n
*L\u1ea5y \u0111i\u1ec3m O thu\u1ed9c tr\u1ee5c \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n
\u0110\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC ti\u1ebfp x\u00fac v\u1edbi BC, CA, AB l\u1ea7n l\u01b0\u1ee3t t\u1ea1i N, P, M, ta c\u00f3: HM \u22a5 AB, HN \u22a5 BC, HP \u22a5 CA<\/p>\n
OM \u22a5 AB, ON \u22a5 BC, OP \u22a5 CA (1)<\/p>\n
M\u1eb7t kh\u00e1c: HM = HN = HP => \u0394OHM = \u0394OHN = \u0394OHP<\/p>\n
OM = ON = OP (2)<\/p>\n
T\u1eeb (1) v\u00e0 (2) suy ra m\u1eb7t c\u1ea7u (S) ti\u1ebfp x\u00fac v\u1edbi ba c\u1ea1nh c\u1ee7a tam gi\u00e1c ABC. V\u1eady t\u1eadp h\u1ee3p t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t c\u1ea7u ti\u1ebfp x\u00fac v\u1edbi ba c\u1ea1nh c\u1ee7a tam gi\u00e1c ABC cho tr\u01b0\u1edbc l\u00e0 tr\u1ee5c \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n
B\u00e0i 5 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0T\u1eeb m\u1ed9t \u0111i\u1ec3m M n\u1eb1m ngo\u00e0i m\u1eb7t c\u1ea7u (O; R), v\u1ebd hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft m\u1eb7t c\u1ea7u l\u1ea7n l\u01b0\u1ee3t t\u1ea1i A, B v\u00e0 C, D.<\/strong><\/span><\/p>\na) Ch\u1ee9ng minh r\u1eb1ng MA.MB = MC.MD<\/strong><\/span><\/p>\nb) G\u1ecdi MO = d. T\u00ednh MA.MB theo R v\u00e0 d.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-5-trang-49-sgk-hinh-hoc-12.png\")
<\/p>\n
a) Hai \u0111\u01b0\u1eddng th\u1eb3ng MAB v\u00e0 MCD giao nhau x\u00e1c \u0111\u1ecbnh m\u1ed9t m\u1eb7t ph\u1eb3ng (P). M\u1eb7t ph\u1eb3ng (P) c\u1eaft m\u1eb7t c\u1ea7u theo giao tuy\u1ebfn l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n (C), ngo\u1ea1i ti\u1ebfp t\u1ee9 gi\u00e1c ph\u1eb3ng ABCD.<\/p>\n
Trong m\u1eb7t ph\u1eb3ng (P) th\u00ec c\u00e1c t\u00edch MA.MB v\u00e0 MC.MD l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a ph\u01b0\u01a1ng t\u00edch c\u1ee7a \u0111i\u1ec3m M \u0111\u1ed1i v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n (C), do \u0111\u00f3:<\/p>\n
MA.MB = MC.MD.<\/p>\n
b) M\u1eb7t ph\u1eb3ng (OAB) c\u1eaft m\u1eb7t c\u1ea7u theo \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn v\u00e0 ph\u01b0\u01a1ng t\u00edch c\u1ee7a \u0111i\u1ec3m M \u0111\u1ed1i v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y l\u00e0 :<\/p>\n
PM\/(O)<\/sub>\u00a0= MA.MB = d2<\/sup>\u00a0– R2<\/sup>(v\u00ec d > R).<\/p>\nB\u00e0i 6 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho m\u1eb7t c\u1ea7u (O; R) ti\u1ebfp x\u00fac v\u1edbi m\u1eb7t ph\u1eb3ng (P) t\u1ea1i I. G\u1ecdi M l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m tr\u00ean m\u1eb7t c\u1ea7u nh\u01b0ng kh\u00f4ng ph\u1ea3i l\u00e0 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi I qua t\u00e2m O. T\u1eeb M ta k\u1ebb hai ti\u1ebfp tuy\u1ebfn c\u1ee7a m\u1eb7t c\u1ea7u c\u1eaft (P) t\u1ea1i A v\u00e0 B. Ch\u1ee9ng minh r\u1eb1ng g\u00f3c (AMB)= g\u00f3c (AIB)<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
\u00a0![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-6-trang-49-sgk-hinh-hoc-12-1.png\")
<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-6-trang-49-sgk-hinh-hoc-12.png\")
<\/p>\n
B\u00e0i 7 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.A’B’C’D’ c\u00f3 AA’ = a, AB = b, AD = c.<\/strong><\/span><\/p>\na) H\u00e3y x\u00e1c \u0111\u1ecbnh t\u00e2m v\u00e0 b\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u \u0111i qua 8 \u0111\u1ec9nh c\u1ee7a h\u00ecnh h\u1ed9p \u0111\u00f3.<\/strong><\/span><\/p>\nb) T\u00ednh b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 giao tuy\u1ebfn c\u1ee7a mp(ABCD) v\u1edbi m\u1eb7t c\u1ea7u tr\u00ean.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-7-trang-49-sgk-hinh-hoc-12.png\")
<\/p>\n
B\u00e0i 8 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng n\u1ebfu c\u00f3 m\u1ed9t m\u1eb7t c\u1ea7u ti\u1ebfp x\u00fac v\u1edbi 6 c\u1ea1nh c\u1ee7a m\u1ed9t h\u00ecnh t\u1ee9 di\u1ec7n th\u00ec t\u1ed5ng c\u00e1c c\u1eb7p c\u1ea1nh \u0111\u1ed1i di\u1ec7n c\u1ee7a t\u1ee9 di\u1ec7n b\u1eb1ng nhau.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-8-trang-49-sgk-hinh-hoc-12.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-8-trang-49-sgk-hinh-hoc-12-1.png\")
<\/p>\n
B\u00e0i 9 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho m\u1ed9t \u0111i\u1ec3m A c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng a c\u1ed1 \u0111\u1ecbnh kh\u00f4ng \u0111i qua A. G\u1ecdi O l\u00e0 m\u1ed9t \u0111i\u1ec3m thay \u0111\u1ed5i tr\u00ean a. Ch\u1ee9ng minh r\u1eb1ng c\u00e1c m\u1eb7t c\u1ea7u t\u00e2m O b\u00e1n k\u00ednh r = OA lu\u00f4n lu\u00f4n \u0111i qua m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u1ed1 \u0111\u1ecbnh<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
G\u1ecdi (P) l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua A v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng a t\u1ea1i H. Khi \u0111\u00f3 (P) v\u00e0 H c\u1ed1 \u0111\u1ecbnh.<\/p>\n
Ta c\u00f3: (P) c\u1eaft m\u1eb7t c\u1ea7u S(O; R) theo \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m H v\u00e0 b\u00e1n k\u00ednh HA kh\u00f4ng \u0111\u1ed5i.<\/p>\n
V\u1eady c\u00e1c m\u1eb7t c\u1ea7u t\u00e2m O b\u00e1n k\u00ednh R = OA lu\u00f4n \u0111i qua \u0111\u01b0\u1eddng tr\u00f2n c\u1ed1 \u0111\u1ecbnh t\u00e2m H b\u00e1n k\u00ednh b\u1eb1ng HA.<\/p>\n
B\u00e0i 10 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p S.ABC c\u00f3 b\u1ed1n \u0111\u1ec9nh \u0111\u1ec1u n\u1eb1m tr\u00ean m\u1ed9t m\u1eb7t c\u1ea7u, SA = a, SB = b, SC = c v\u00e0 ba c\u1ea1nh SA, SB, SC \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c. T\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u \u0111\u01b0\u1ee3c t\u1ea1o n\u00ean b\u1edfi m\u1eb7t c\u1ea7u \u0111\u00f3.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-10-trang-49-sgk-hinh-hoc-12.png\")
<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-10-trang-49-sgk-hinh-hoc-12-1.png\")
<\/p>\n
<\/p>\n
<\/div>\n","protected":false},"excerpt":{"rendered":"
B\u00e0i 1 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0T\u00ecm t\u1eadp h\u1ee3p t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m M trong kh\u00f4ng gian lu\u00f4n lu\u00f4n nh\u00ecn m\u1ed9t \u0111o\u1ea1n th\u1eb3ng AB c\u1ed1 \u0111\u1ecbnh d\u01b0\u1edbi m\u1ed9t g\u00f3c vu\u00f4ng. L\u1eddi gi\u1ea3i: B\u00e0i 2 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 c\u1ea1nh \u0111\u1ec1u b\u1eb1ng a. X\u00e1c \u0111\u1ecbnh t\u00e2m […]<\/p>\n","protected":false},"author":3,"featured_media":20555,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1377,1356,1355],"yoast_head":"\n
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L\u1eddi gi\u1ea3i: B\u00e0i 2 (trang 49 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 c\u1ea1nh \u0111\u1ec1u b\u1eb1ng a. 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