Interior bisectors

[MareX]

Show that if the bisectors of three interior angles of a convex quadrilateral ABCD intersect at a point P, then P is also on the fourth interior bisector.

 

[Dr.Peterson]

Suppose the angle bisectors of A, B, and C meet at P. Construct perpendiculars from P to each of the sides of ABCD, and think about how they are related.