IR-TST 2018 Problem 11

Let $\omega$ be the circumcircle of isosceles triangle $ABC$ ( $AB=AC$ ). Points $P$ and $Q$ lie on $\omega$ and $BC$ respectively such that $AP=AQ$ . $AP$ and $BC$ intersect at $R$ . Prove that the tangents from $B$ and $C$ to the incircle of $\triangle AQR$ (different from $BC$ ) are concurrent on $\omega$ .

Proposed by Ali Zamani, Hooman Fattahi