B\u00e0i t\u1eadp H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy (H\u00ecnh gi\u1ea3i t\u00edch trong m\u1eb7t ph\u1eb3ng) l\u00e0 m\u1ed9t b\u00e0i kh\u00f3, th\u01b0\u1eddng l\u00e0 c\u00e2u l\u1ea5y \u0111i\u1ec3m 8 nh\u01b0ng \u0111\u00f4i khi c\u0169ng l\u00e0 c\u00e2u l\u1ea5y \u0111i\u1ec3m 9 trong \u0111\u1ec1 thi THPT qu\u1ed1c gia.<\/p>\n

R\u1ea5t nhi\u1ec1u h\u1ecdc sinh l\u00e0m \u0111\u01b0\u1ee3c c\u00e2u l\u1ea5y \u0111i\u1ec3m 9 (Ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 t\u1ec9, B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 t\u1ec9, H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh) nh\u01b0ng kh\u00f4ng l\u00e0m \u0111\u01b0\u1ee3c c\u00e2u H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy. Nguy\u00ean nh\u00e2n l\u00e0 do c\u00e2u l\u1ea5y \u0111i\u1ec3m 9 th\u01b0\u1eddng c\u00f3 nh\u1eefng d\u1ea1ng c\u1ee5 th\u1ec3, c\u00e1c d\u1ea5u hi\u1ec7u \u0111\u00e3 \u0111\u01b0\u1ee3c khai th\u00e1c nhi\u1ec1u, h\u1ecdc sinh c\u1ea7n c\u00f3 t\u01b0 duy t\u1ed1t v\u00e0 \u00f4n luy\u1ec7n \u0111\u1ea7y \u0111\u1ee7 c\u00e1c d\u1ea1ng v\u00e0 k\u0129 thu\u1eadt gi\u1ea3i to\u00e1n th\u00ec kh\u1ea3 n\u0103ng l\u00e0m \u0111\u01b0\u1ee3c l\u00e0 kh\u00e1 cao.<\/p>\n

<\/p>\n

Trong khi \u0111\u00f3, \u0111\u1eb7c th\u00f9 m\u00f4n H\u00ecnh h\u1ecdc l\u00e0 kh\u00f4ng c\u00f3 nhi\u1ec1u d\u1ea1ng c\u1ee5 th\u1ec3 m\u1ed9t c\u00e1ch r\u00f5 r\u00e0ng. N\u00ean h\u1ecdc sinh l\u00fac \u00f4n thi th\u01b0\u1eddng kh\u00f4ng c\u00f3 c\u00e1i nh\u00ecn t\u1ed5ng qu\u00e1t v\u1ec1 nh\u1eefng ph\u1ea7n ki\u1ebfn th\u1ee9c s\u1ebd thi. Khi l\u00e0m b\u00e0i th\u01b0\u1eddng d\u1ef1a v\u00e0o s\u1ef1 may m\u1eafn.<\/p>\n

\u0110\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c b\u00e0i t\u1eadp H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy, th\u1ea7y Nguy\u1ec5n B\u00e1 Tu\u1ea5n \u0111\u01b0a ra m\u1ed9t v\u00e0i l\u1eddi khuy\u00ean sau:<\/p>\n

– C\u00e2u H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy th\u01b0\u1eddng s\u1ebd c\u00f3 hai m\u1ee9c \u0111\u1ed9. M\u1ee9c \u0111\u1ed9 1 th\u01b0\u1eddng cho c\u00e1c em t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t d\u1eef ki\u1ec7n n\u00e0o \u0111\u00f3 l\u1ea5y 0,25\u0111. Khi l\u00e0m b\u00e0i, ch\u00fang ta t\u00ecm \u0111\u01b0\u1ee3c c\u00e1c t\u1ecda \u0111\u1ed9 c\u00e1c \u0111i\u1ec3m (ho\u1eb7c vi\u1ec7c tham s\u1ed1 c\u00e1c t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m theo \u1ea9n), hay vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng, t\u00ednh kho\u1ea3ng c\u00e1ch…. th\u00f4ng qua c\u00e1c d\u1eef ki\u1ec7n cho tr\u01b0\u1edbc l\u00e0 c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c 0,25 \u0111i\u1ec3m.<\/p>\n

– V\u1ea5n \u0111\u1ec1 m\u1ea5u ch\u1ed1t trong c\u00e2u H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy th\u01b0\u1eddng l\u00e0 m\u1ed9t t\u00ednh ch\u1ea5t v\u1ec1 s\u1ef1 vu\u00f4ng g\u00f3c, b\u1eb1ng nhau (\u0111o\u1ea1n th\u1eb3ng b\u1eb1ng nhau ho\u1eb7c g\u00f3c b\u1eb1ng nhau) ho\u1eb7c 1 t\u1ec9 l\u1ec7 xoay quanh nh\u1eefng d\u1eef ki\u1ec7n \u0111\u00e3 bi\u1ebft. \u0110\u1ec3 t\u00ecm ra t\u00ednh ch\u1ea5t quan tr\u1ecdng \u0111\u00f3 ta c\u00f3 m\u1ea5y l\u01b0u \u00fd nh\u01b0 sau:<\/p>\n

+ V\u1ebd h\u00ecnh th\u1eadt ch\u00ednh x\u00e1c;<\/p>\n

+ C\u00f3 th\u1ec3 v\u1ebd nhi\u1ec1u h\u00ecnh, ho\u1eb7c v\u1ebd nh\u1eefng tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t \u0111\u1ec3 r\u00fat ra c\u00e1c quy lu\u1eadt chung t\u1eeb c\u00e1c h\u00ecnh \u0111\u00f3;<\/p>\n

+ D\u00e0nh th\u1eddi gian \u00f4n luy\u1ec7n c\u00e1c b\u00e0i to\u00e1n THCS c\u00f3 li\u00ean quan \u0111\u1ebfn tam gi\u00e1c, c\u00e1c h\u00ecnh t\u1ee9 gi\u00e1c, c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan t\u1edbi \u0111\u01b0\u1eddng tr\u00f2n… V\u1edbi m\u1ed7i b\u00e0i to\u00e1n n\u00ean ghi nh\u1edb l\u1ea1i c\u00e1c t\u00ednh ch\u1ea5t \u0111\u1eb7c tr\u01b0ng v\u00e0 c\u00e1ch ch\u1ee9ng minh. Vi\u1ec7c ghi nh\u1edb l\u1ea1i n\u00ean l\u00e0m t\u01b0\u01a1ng t\u1ef1 khi gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc ph\u1eb3ng trong c\u00e1c \u0111\u1ec1 thi th\u1eed c\u1ee7a nhi\u1ec1u tr\u01b0\u1eddng.<\/p>\n

+ C\u00e1c d\u1eef ki\u1ec7n \u0111\u1ec1 b\u00e0i \u0111\u1ec1u c\u00f3 m\u1ee5c \u0111\u00edch c\u1ee7a n\u00f3. N\u1ebfu quan s\u00e1t b\u00e0i to\u00e1n m\u00e0 kh\u00f4ng t\u00ecm th\u1ea5y h\u01b0\u1edbng \u0111i n\u00e0o th\u00ec n\u00ean g\u1eafn k\u1ebft c\u00e1c d\u1eef ki\u1ec7n l\u1ea1i m\u00e0 \u0111\u1ec1 b\u00e0i cho l\u1ea1i v\u1edbi nhau. V\u00ed d\u1ee5, cho t\u1ecda \u0111\u1ed9 2 \u0111i\u1ec3m A, B th\u00ec s\u1ebd vi\u1ebft \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng AB, x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n AB, vi\u1ebft \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng vu\u00f4ng v\u1edbi AB t\u1ea1i A, B hay x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c trung \u0111i\u1ec3m c\u1ee7a AB… C\u00f9ng v\u1edbi k\u1ebft h\u1ee3p c\u00e1c d\u1eef ki\u1ec7n c\u00f2n l\u1ea1i s\u1ebd t\u1ea1o ra c\u00e1c \u00fd t\u01b0\u1edfng, h\u01b0\u1edbng \u0111i ti\u1ebfp theo.<\/p>\n

+ Qu\u00e1 tr\u00ecnh gi\u1ea3i l\u00e0 qu\u00e1 tr\u00ecnh t\u00ecm \u0111i\u1ec3m, t\u00ecm \u0111\u01b0\u1eddng m\u1ed9t c\u00e1ch c\u00f3 th\u1ee9 t\u1ef1. C\u1ea7n xem nh\u1eefng \u0111i\u1ec3m n\u00e0o n\u1eb1m tr\u00ean nh\u1eefng \u0111\u01b0\u1eddng cho tr\u01b0\u1edbc \u0111\u1ec3 \u01b0u ti\u00ean t\u00ecm \u0111\u1ea7u ti\u00ean, c\u0169ng d\u1ef1a v\u00e0o nh\u1eefng \u0111i\u1ec3m \u0111\u00f3 \u0111\u1ec3 x\u00e2y d\u1ef1ng l\u00ean t\u00ednh ch\u1ea5t c\u1ed1t l\u00f5i m\u00e0 b\u00e0i to\u00e1n ng\u1ea7m \u0111\u1ec3 trong \u0111\u00f3.<\/p>\n

V\u00ed d\u1ee5 1: Cho tam gi\u00e1c ABC n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m I(2;1), b\u00e1n k\u00ednh . Bi\u1ebft ch\u00e2n \u0111\u01b0\u1eddng cao h\u1ea1 t\u1eeb c\u00e1c \u0111\u1ec9nh B, C \u0111\u1ebfn AC v\u00e0 AB l\u1ea7n l\u01b0\u1ee3t l\u00e0 K(-2;3) v\u00e0 . T\u00ecm t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh tam gi\u00e1c.<\/strong><\/em><\/p>\n

\nH\u01b0\u1edbng d\u1eabn gi\u1ea3i nhanh b\u00e0i t\u1eadp H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy trong \u0111\u1ec1 thi THPT qu\u1ed1c gia – \u1ea3nh 1
\n+ Khi c\u00e1c em nh\u1edb \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t AI vu\u00f4ng g\u00f3c v\u1edbi HK th\u00ec b\u00e0i to\u00e1n tr\u1edf l\u00ean nh\u1eb9 nh\u00e0ng, trong tr\u01b0\u1eddng h\u1ee3p kh\u00f4ng nh\u1edb th\u00ec th\u1ef1c hi\u1ec7n vi\u1ec7c v\u1ebd h\u00ecnh chu\u1ea9n x\u00e1c ho\u1eb7c v\u1ebd th\u00eam 1 h\u00ecnh kh\u00e1c \u0111\u1ec3 quan s\u00e1t t\u00ednh ch\u1ea5t c\u1ed1 \u0111\u1ecbnh trong h\u00ecnh l\u00e0 1 \u0111i\u1ec1u r\u1ea5t c\u1ea7n thi\u1ebft.
\n+ Vi\u1ec7c ph\u00e1t hi\u1ec7n t\u00ednh ch\u1ea5t trong h\u00ecnh ta c\u0169ng n\u00ean k\u1ebft h\u1ee3p th\u00eam vi\u1ec7c g\u1eafn k\u1ebft t\u1edbi c\u00e1c d\u1eef ki\u1ec7n m\u00e0 \u0111\u1ec1 b\u00e0i \u0111\u00e3 cho. Trong b\u00e0i tr\u00ean ta \u0111\u00e3 bi\u1ebft t\u1ecda \u0111\u1ed9 3 \u0111i\u1ec3m H, K, I c\u00f9ng b\u00e1n k\u00ednh IA=IB=IC. Nh\u01b0 v\u1eady n\u1ebfu t\u1ecda \u0111\u1ed9 3 \u0111\u1ec9nh \u0111\u01b0\u1ee3c tham s\u1ed1 qua 1 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng th\u00ec b\u00e0i to\u00e1n \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft. C\u00e1c ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y s\u1ebd ph\u1ea3i \u0111i qua t\u1ecda \u0111\u1ed9 c\u00e1c \u0111i\u1ec3m m\u00e0 \u0111\u1ec1 b\u00e0i \u0111\u00e3 cho => c\u1ea7n th\u00eam 1 vector ph\u00e1p tuy\u1ebfn ho\u1eb7c vector ch\u1ec9 ph\u01b0\u01a1ng hay 1 y\u1ebfu t\u1ed1 v\u1ec1 g\u00f3c, kho\u1ea3ng c\u00e1ch => quan s\u00e1t c\u00e1c t\u00ednh ch\u1ea5t v\u1ec1 \/\/ ho\u1eb7c vu\u00f4ng g\u00f3c trong h\u00ecnh v\u1ebd cho ta s\u1ef1 ph\u00e1t hi\u1ec7n v\u1ec1 y\u1ebfu t\u1ed1 ho\u1eb7c quan s\u00e1t xem BI c\u00f3 th\u1ec3 \/\/ v\u1edbi HK \u0111\u01b0\u1ee3c hay kh\u00f4ng?<\/p>\n

Khi ph\u00e1t hi\u1ec7n \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t r\u1ed3i th\u00ec vi\u1ec7c \u0111i ch\u1ee9ng minh t\u00ednh ch\u1ea5t \u0111\u00f3 c\u0169ng l\u00e0 1 c\u00f4ng vi\u1ec7c r\u1ea5t quan tr\u1ecdng. Vi\u1ec7c ch\u1ee9ng minh th\u01b0\u1eddng kh\u00f4ng kh\u00f3 song v\u1eabn c\u1ea7n n\u1eafm ch\u1eafc c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 s\u1edf trong ch\u01b0\u01a1ng tr\u00ecnh THCS.<\/p>\n

T\u1eeb I k\u1ebb IM vu\u00f4ng g\u00f3c v\u1edbi AC t\u1ea1i M khi \u0111\u00f3 ta c\u00f3<\/p>\n

M\u1eb7t kh\u00e1c do t\u1ee9 gi\u00e1c BCKH n\u1ed9i ti\u1ebfp =><\/p>\n

M\u00e0 hay AI vu\u00f4ng g\u00f3c v\u1edbi KH<\/p>\n

+ Trong b\u00e0i to\u00e1n th\u01b0\u1eddng c\u00f3 nh\u1eefng \u0111i\u1ec1u ki\u1ec7n v\u1ec1 ho\u00e0nh \u0111\u1ed9 (ho\u1eb7c tung \u0111\u1ed9 \u0111\u1ed1i v\u1edbi \u0111i\u1ec3m n\u00e0o \u0111\u00f3 ) th\u00ec \u0111\u00f3 c\u0169ng l\u00e0 m\u1ed9t g\u1ee3i \u00fd \u1edf \u0111\u1ec1 b\u00e0i v\u1ec1 vi\u1ec7c s\u1ebd t\u00ecm \u0111\u1ebfn \u0111i\u1ec3m \u0111\u00f3. C\u00e1c em l\u01b0u \u00fd l\u00e0 nh\u1eefng d\u1eef ki\u1ec7n nh\u01b0 v\u1eady ch\u1ec9 c\u00f3 t\u00ednh lo\u1ea1i b\u1edbt nghi\u1ec7m h\u00ecnh. C\u00f3 nhi\u1ec1u b\u1ea1n lo xa, hay coi nh\u1eefng d\u1eef ki\u1ec7n nh\u01b0 th\u1ebf quan tr\u1ecdng h\u01a1n m\u1ee9c \u0111\u1ed9 th\u1ef1c s\u1ef1 c\u1ee7a n\u00f3.<\/p>\n

+ Ngo\u00e0i ra c\u00e1c em n\u00ean th\u00e0nh th\u1ea1o c\u00e1c b\u00e0i to\u00e1n nh\u1ecf: nh\u01b0 vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng li\u00ean quan t\u1edbi (\u0111i\u1ec3m, kho\u1ea3ng c\u00e1ch), (\u0111i\u1ec3m, g\u00f3c), (\u0111i\u1ec3m, \u0111\u01b0\u1eddng tr\u00f2n), (kho\u1ea3ng c\u00e1ch, \u0111\u01b0\u1eddng tr\u00f2n)… Khi \u0111\u1ee9ng ri\u00eang r\u1ebd th\u00ec \u0111\u00f3 l\u00e0 c\u00e1c b\u00e0i to\u00e1n r\u1ea5t \u0111\u01a1n gi\u1ea3n xong vi\u1ec7c k\u1ebft h\u1ee3p n\u00f3 v\u00e0o trong c\u00e1c h\u00ecnh ph\u1eb3ng l\u00e0m n\u00f3 tr\u1edf l\u00ean ph\u1ee9c t\u1ea1p h\u01a1n, kh\u00f3 nh\u00ecn nh\u1eadn ra.<\/p>\n

V\u00ed d\u1ee5 2: Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 , cho tam gi\u00e1c c\u00f3 , tr\u1ef1c t\u00e2m v\u00e0 . G\u1ecdi l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u00e2n \u0111\u01b0\u1eddng cao k\u1ebb t\u1eeb . Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng bi\u1ebft \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua .<\/strong><\/em><\/p>\n

<\/p>\n

H\u01b0\u1edbng d\u1eabn gi\u1ea3i nhanh b\u00e0i t\u1eadp H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy trong \u0111\u1ec1 thi THPT qu\u1ed1c gia – \u1ea3nh 2
\nNgo\u00e0i vi\u1ec7c ph\u00e1t hi\u1ec7n v\u00e0 ch\u1ee9ng minh t\u00ednh ch\u1ea5t MN vu\u00f4ng EF th\u00ec h\u01b0\u1edbng \u0111i ti\u1ebfp theo c\u00f3 nhi\u1ec1u b\u1ea1n s\u1ebd v\u1eabn c\u00f2n g\u1eb7p kh\u00f3 kh\u0103n.
\n\u1ede b\u00e0i to\u00e1n n\u00e0y khi MN vu\u00f4ng EF ta s\u1ebd t\u00ednh \u0111\u01b0\u1ee3c \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng EF th\u00f4ng qua tam gi\u00e1c vu\u00f4ng NEM (NE=AH\/2, EM=BC\/2).<\/p>\n

Nh\u01b0 v\u1eady ta d\u1ec5 d\u00e0ng x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c E, F th\u00f4ng qua c\u00e1ch gi\u1ea3i b\u00e0i to\u00e1n nh\u1ecf:<\/p>\n

Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua K c\u1eaft \u0111\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh AH 1 kho\u1ea3ng c\u00f3 \u0111\u1ed9 d\u00e0i EF (do EHFA n\u1ed9i ti\u1ebfp).<\/p>\n

Th\u1ea7y Nguy\u1ec5n B\u00e1 Tu\u1ea5n, Gi\u1ea3ng vi\u00ean \u0110\u1ea1i h\u1ecdc C\u00f4ng nghi\u1ec7p H\u00e0 N\u1ed9i<\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i t\u1eadp H\u00ecnh h\u1ecdc ph\u1eb3ng Oxy (H\u00ecnh gi\u1ea3i t\u00edch trong m\u1eb7t ph\u1eb3ng) l\u00e0 m\u1ed9t b\u00e0i kh\u00f3, th\u01b0\u1eddng l\u00e0 c\u00e2u l\u1ea5y \u0111i\u1ec3m 8 nh\u01b0ng \u0111\u00f4i khi c\u0169ng l\u00e0 c\u00e2u l\u1ea5y \u0111i\u1ec3m… <\/p>\n","protected":false},"author":1,"featured_media":3545,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,75,9],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts\/3543"}],"collection":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/comments?post=3543"}],"version-history":[{"count":0,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/posts\/3543\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/media\/3545"}],"wp:attachment":[{"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/media?parent=3543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/categories?post=3543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/onthitot.com\/wp-json\/wp\/v2\/tags?post=3543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}