CN-TST 2015 Problem 1

The circle $\Gamma$ through $A$ of triangle $ABC$ meets sides $AB,AC$ at $E$ , $F$ respectively, and circumcircle of $ABC$ at $P$ . Prove: Reflection of $P$ across $EF$ is on $BC$ if and only if $\Gamma$ passes through $O$ (the circumcentre of $ABC$ ).