Question 79
Let $\gamma_1$ and $\gamma_2$ be externally tangent circles and $S$ be the point of tangency. Let $\omega$ be a circle that touches internally $\gamma_1$ and $\gamma_2$ at $P$ and $Q$ respectively. Denote by $R$ one of the intersection points of $\omega$ and the common tangent line of $\gamma_1$ and $\gamma_2$ that passes through $S$. Furthermore, the lines $RP$ and $RQ$ intersect $\gamma_1$ and $\gamma_2$ at $A$ and $B$ respectively and the line $PQ$ intersects $\gamma_1$ and $\gamma_2$ at $C$ and $D$ respectively. Prove that the lines $RS$, $AC$ and $BD$ have a common point.