KURSCHAK 2014 Problem 2

We are given an acute triangle $ABC$ , and inside it a point $P$ , which is not on any of the heights $AA_1$ , $BB_1$ , $CC_1$ . The rays $AP$ , $BP$ , $CP$ intersect the circumcircle of $ABC$ at points $A_2$ , $B_2$ , $C_2$ . Prove that the circles $AA_1A_2$ , $BB_1B_2$ and $CC_1C_2$ are concurrent.