OLYMPIC-REVENGE 2017 Problem 2

Let $\triangle$ $ABC$ a triangle with circumcircle $\Gamma$ . Suppose there exist points $R$ and $S$ on sides $AB$ and $AC$ , respectively, such that $BR=RS=SC$ . A tangent line through $A$ to $\Gamma$ meet the line $RS$ at $P$ . Let $I$ the incenter of triangle $\triangle$ $ARS$ . Prove that $PA=PI$