ZA-SAMO 2012 Problem 5

Let $ABC$ be a triangle such that $AB\neq AC$ . We denote its orthocentre by $H$ , its circumcentre by $O$ and the midpoint of $BC$ by $D$ . The extensions of $HD$ and $AO$ meet in $P$ . Prove that triangles $AHP$ and $ABC$ have the same centroid.