Question 10
Let $ABC$ be a triangle with $\hat{C} = 60^\circ$. The point $P$ is the symmetrical point of $A$ with respect to the point of tangency of the circle inscribed with the side $BC$. Prove that if the bisector of the segment $CP$ cuts the line containing the bisector of the angle $\hat{B}$ at the point $Q$, then the triangle $CPQ$ is equilateral.