# Geometry, Equilateral triangle

Let $P$ be point lie on circumcircle of an equilateral triangle $\Delta ABC$.

Let $D, E, F$ be projection points from $P$ to $BC, CA, AB$.

$a)$ Prove that $\displaystyle AD^2+BE^2+CF^2=\frac{33}{4}.R^2$

$b)$ Prove that $\displaystyle AD^4+BE^4+CF^4=\frac{369}{16}.R^4$

Author: Van Khea, Cambodia