Question

Demonstrati ca intr-un triunghi are loc relatia 1/hA+1/hB+1/hC=1/r.

Answer 1

$\it \dfrac{1}{h_a} + \dfrac{1}{h_b} + \dfrac{1}{h_c} = \dfrac{a}{2S} + \dfrac{b}{2S} + \dfrac{c}{2S} = \dfrac{a+b+c}{2S} = \dfrac{2p}{2pr} =\dfrac{1}{r}$