MathNet 2010 — Part 01 Question 100

Circles $\Gamma_1$ and $\Gamma_2$ touch each other externally at point $M_3$. They touch a circle $\Gamma_3$ internally at points $M_1$ and $M_2$ respectively. Let $S$ be the circumcenter of the triangle $M_1M_2M_3$. Prove that the line $SM_1$ touches $\Gamma_3$.
(M. Karpuk)