Cho Δ ABC có 3 góc nhọn nội tiếp đường tròn (O) . Các đường cao AD,BI, CK cắt nhau tại H. tìm gtnn của bt 
T=ADHD+BIHI+CKHK
lại hình 9 –  ๖ۣۜJinღ๖ۣۜKaido 04-11-15 07:01 PM
T=ADHD+BIHI+CKHK9HDAD+HIBI+HKCK=9SHBCSABC+SHACSABC+SHABSABC=9
Dấu "=" xảy ra khi và chỉ khi \frac{AD}{HD}=\frac{BI}{HI}=\frac{CK}{HK}
Điều này chỉ xảy ra khi AD,BI,CK là các đường trung tuyến mà chúng lại là đường cao
Vậy GTNN của T9 khi \triangle ABC là tam giác đều

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