# author by vankhea

Let $P$ be any point inside of $\Delta ABC$. Let $AP, BP, CP$ cuts $BC, CA, AB$ at $D, E, F$ and cuts circumcircle of $\Delta ABC$ at $X, Y, Z$.

Prove that: $\displaystyle (\frac{XP}{PA}+\frac{YP}{PB}+\frac{ZP}{PC})(\frac{AD}{DX}+\frac{BE}{EY}+\frac{CF}{FZ})\geq 27$

Author: Van Khea