Question

Cho tam giác ABC, b + c = 2a thì \(\dfrac{2}{AH}=\dfrac{1}{HB}+\dfrac{1}{HC}\)

Answer 1

Có : \(S=\dfrac{1}{2}h_aa=\dfrac{1}{2}h_bb=\dfrac{1}{2}h_cc\)

\(\Rightarrow\left\{{}\begin{matrix}h_a=\dfrac{2S}{a}\\h_b=\dfrac{2S}{b}\\h_c=\dfrac{2S}{c}\end{matrix}\right.\)

\(\Rightarrow VT=\dfrac{b}{2S}+\dfrac{c}{2S}=\dfrac{b+c}{2S}=\dfrac{2a}{2S}=\dfrac{2}{h_a}\)

=> ĐPCM