Cho tam giác ABC nhọn . Vẽ về phía ngoài tam giác ba tam giác đều BCA', CAB', ABC' . Chứng minh : AA', BB', CC' đồng quy
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Câu hỏi của Nguyễn Thị Thùy Dung - Toán lớp 9 | Học trực tuyến
9 tháng 5 2015
chỗ nào bạn ko hiểu ở bài này cứ hỏi mình ,mình giải hơi vắng tắt
tam giác aba'=tg c'bc (c.g.c)(do c'b=ab ;ba'=bc',góc 'bc=aba')suy ra cc'=aa'
tương tự ta có tam giác c'ac =b'ab suy ra cc'=bb'
từ 2 dòng trên suy ra aa'=bb'=cc'
15 tháng 6 2022
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Câu hỏi của Nguyễn Thị Thùy Dung - Toán lớp 9 | Học trực tuyến
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Câu hỏi của Nguyễn Thị Thùy Dung - Toán lớp 9 | Học trực tuyến
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Câu hỏi của Nguyễn Thị Thùy Dung - Toán lớp 9 | Học trực tuyến
VB
24 tháng 1 2020
Gọi O là giao điểm của AA1 và CC1. Ta chứng minh \(\widehat{AOB}+\widehat{AOB_1}=180^o\).
Ta có: \(\Delta C_1BC=\Delta ABA_1\) vì \(C_1B=AB\), BC=BA1, góc C1BC = góc ABA1 (=góc ABC+60độ).
Suy ra \(\widehat{BC_1C}=\widehat{BAA_1}\) suy tiếp \(C_1BOA\) là tứ giác nội tiếp đường tròn.
\(\Rightarrow\widehat{AC_1B}+\widehat{AOB}=180^o\) \(\Rightarrow\widehat{AOB}=120^o\) và \(\widehat{C_1OB}=\widehat{C_1OA}=60^o\) (cùng chắn hai cung có độ dài bằng nhau).
Tương tự ta có các góc AOB1, B1OC, COA1, A1OB đều bằng 60 độ.
Suy ra \(\widehat{AOB}+\widehat{AOB_1}=180^o\)
Vậy BOB1 thẳng hàng