OBM 2015 Problem 6

Let $\triangle ABC$ be a scalene triangle and $X$ , $Y$ and $Z$ be points on the lines $BC$ , $AC$ and $AB$ , respectively, such that $\measuredangle AXB = \measuredangle BYC = \measuredangle CZA$ . The circumcircles of $BXZ$ and $CXY$ intersect at $P$ . Prove that $P$ is on the circumference which diameter has ends in the ortocenter $H$ and in the baricenter $G$ of $\triangle ABC$ .