Question 131
The circles $\omega_1$ and $\omega_2$ which do not intersect and which have different sizes are tangent to the line $\ell$ at $K$ and $L$, and are tangent to the circle $\Gamma$ at $M$ and $N$ respectively, such that all three circles lie on the same side of $\ell$. A circle which passes through $K$ and $L$ intersects $\Gamma$ at $A$ and $B$. The reflections of $M$ and $N$ over $\ell$ are $R$ and $S$ respectively. Show that the points $A, B, R, S$ are concyclic.