RIOPLATENSE 2002 Problem 3

Let $ABC$ be a triangle with $\angle C=60^o$ . The point $P$ is the symmetric of $A$ with respect to the point of tangency of the circle inscribed with the side $BC$ . Show that if the perpendicular bisector of the $CP$ segment intersects the line containing the angle - bisector of $\angle B$ at the point $Q$ , then the triangle $CPQ$ is equilateral.