OMCPLP 2013 Problem 6

Consider a triangle $ABC$ . Let $S$ be a circumference in the interior of the triangle that is tangent to the sides $BC$ , $CA$ , $AB$ at the points $D$ , $E$ , $F$ respectively. In the exterior of the triangle we draw three circumferences $S_A$ , $S_B$ , $S_C$ . The circumference $S_A$ is tangent to $BC$ at $L$ and to the prolongation of the lines $AB$ , $AC$ at the points $M$ , $N$ respectively. The circumference $S_B$ is tangent to $AC$ at $E$ and to the prolongation of the line $BC$ at $P$ . The circumference $S_C$ is tangent to $AB$ at $F$ and to the prolongation of the line $BC$ at $Q$ . Show that the lines $EP$ , $FQ$ and $AL$ meet at a point of the circumference $S$ .