Let $ABC$ be an acute triangle and let $X, Y , Z$ denote the midpoints of the shorter arcs $BC, CA, AB$ of its circumcircle, respectively. Let $M$ be an arbitrary point on side $BC$. The line through $M$, parallel to the inner angular bisector of $\angle CBA$ meets the outer angular bisector of $\angle BCA$ at point $N$. The line through $M$, parallel to the inner angular bisector of $\angle BCA$ meets the outer angular bisector of $\angle CBA$ at point $P$. Prove that lines $XM, Y N, ZP$ pass through a single point.