The point M is the center of a regular pentagon ABCDE. The point P is an inner point of the line segment [DM]. The circumscribed circle of triangle △ABP intersects the side [AE] at point Q (different from A). The perpendicular from P on CD intersects the side [AE] at point S. Prove that PS is the bisector of ∠APQ. geometryangle bisectorpentagon