# An equilateral triangle ABC

Let $O$ be circumcenter of an equilateral triangle $\Delta ABC$ and let $P$ be point lie on incircle. Prove that:

$a)$ $PD=PE+PF$

$b)$ $PD^2+PE^2+PF^2=3R^2$

$c)$ $PD^4+PE^4+PF^4=\frac{9}{2}.R^4$

Author: Van Khea, Cambodia