mathschallenge.net

Problem

It can be shown that a unique circle passes through three given points. In triangle ABC three points $A'$, $B'$, and $C'$ lie on the edges opposite $A$, $B$, and $C$ respectively.

Given that the circle $AB'C'$ intersects circle $BA'C'$ inside the triangle at point $P$, prove that circle $CA'B'$ will be concurrent with point $P$.