Problem

Source: Iranian TST 2018, second exam day 2, problem 5

Tags: geometry



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 fromĀ $BC$) are concurrent on $\omega$. Proposed by Ali Zamani, Hooman Fattahi