XI APMO

Let ${\Gamma }_1$ and ${\Gamma }_2$ be two circles intersecting at $P$ and $Q$. The common tangent, closer to $P$, of ${\Gamma }_1$ and ${\Gamma }_2$ touches ${\Gamma }_1$ at $A$ and ${\Gamma }_2$ at $B$. The tangent of ${\Gamma }_1$ at $P$ meets ${\Gamma }_2$ at $C$, which is different from $P$ and the extension of $AP$ meets $BC$ at $R$. Prove that the circumcircle of triangle $PQR$ is tangent to $BP$ and $BR$.