Question 3
Let $\Gamma_1,\Gamma_2$ be two circles intersecting at $P,Q$. Their common tangent closer to $P$ touches $\Gamma_1$ at $A$ and $\Gamma_2$ at $B$. The tangent to $\Gamma_1$ at $P$ meets $\Gamma_2$ again at $C\ne P$, and the extension of $AP$ meets $BC$ at $R$. Prove that the circumcircle of $PQR$ is tangent to $BP$ and $BR$.
