Given a triangle AABC and a point P in the triangle. Let L be a line through this point P, perpendicular to AB and let D be the intersection point of the line L and side AB. Let M be another line through P that is perpendicular to the side AC and let the point E be the intersection point of the line M and the side AC. Prove that P lies on the bisector of the angle ZBAC if and only if |PE| = |PD|. Using Pythagorean theorem and the angle sum of a triangle?