KöMaL 2005 A377

The inscribed circle of the triangle ABC touches the side $AB$ at $C_1$, the side $BC$at $A_1$, and the side $CA$ at $B_1$. It is known that the line segments $AA_1$, $BB_1$ and $CC_1$ pass through a common point. Let $N$ denote that point. Draw the three circles that pass through $N$ and touches two of the sides. Prove that the six points of tangency are concyclic.