Question 2
Two circles $\Gamma_1,\Gamma_2$ with radii $r_1,r_2$, respectively, touch internally at the point $P$. A tangent parallel to the diameter through $P$ touches $\Gamma_1$ at $R$ and intersects $\Gamma_2$ at $M$ and $N$. Prove that $PR$ bisects $\angle MPN$.
