Proving colinearity of 3 points(basic Euclidean geometry)

Question

In the above image, AP is bisector of the angle BAC and DP is a perpendicular bisector of the segment BC.

How can it be proved that the points E, D, F are colinear?

Answer 1

Note that $P$ is the mid-point of the minor arc BC of the circumcircle ABC. So EDF is the Simson line of the point $P$.