CN-LEAGUE 2017 Problem 1

Given an isocleos triangle $ABC$ with equal sides $AB=AC$ and incenter $I$ .Let $\Gamma_1$ be the circle centered at $A$ with radius $AB$ , $\Gamma_2$ be the circle centered at $I$ with radius $BI$ .A circle $\Gamma_3$ passing through $B,I$ intersects $\Gamma_1$ , $\Gamma_2$ again at $P,Q$ (different from $B$ ) respectively.Let $R$ be the intersection of $PI$ and $BQ$ .Show that $BR \perp CR$ .