# Centroid G of ABC: Author Van Khea

Let $G$ be the centroid of $\Delta ABC$. Let $AG, BG, CG$ cuts $BC, CA, AB$ at $D, E, F$ and cuts circumcircle of $\Delta ABC$ at $X, Y, Z$. Let $YZ, ZX, XY$ cuts $AG, BG, CG$ at $P, Q, R$.

a) Prove that: $\displaystyle \frac{GD}{GX}+\frac{GE}{GY}+\frac{GF}{GZ}=\frac{3}{2}$

b) Prove that: $\displaystyle \frac{GD}{GP}+\frac{GE}{GQ}+\frac{GF}{GR}=3$

Author: Van Khea