Cho tam giác nhọn ABC; M,N,P lần lượt là các điểm trên cạnh BC, CA, AB. Gọi E,F lần lượt là các điểm đối xứng của M qua AB, AC và AI là đường cao tam giác ABC. Chứng minh chu vi tam giác $MNP\geqslant EF\geqslant 2AI.sinA$.
bài này khó ghê –  congiola_ktqd 07-11-12 08:48 PM

Ta có:
$MN+NP+PM=EN+NP+PF\geq EF$
Dễ thấy $\widehat{EAF}=2\widehat{BAC}=2A$. Ta có:
$\frac{EF}{AE}=\frac{\sin 2A}{\sin (90^0-A)}=2\sin A$
Từ đó suy ra $EF=2AE\sin A=2AM\sin A\geq 2AI\sin A.$
vote cho bạn –  anhkute_02 07-11-12 09:46 AM
bạn vẽ dc cả hình nữa cơ ah, giỏi thế –  anhkute_02 07-11-12 09:46 AM

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