# Proving colinearity of 3 points(basic Euclidean geometry)

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?

• You cannot in general ! because it is true only for some special position of $BC$ – Emilio Novati Dec 3 '18 at 10:29
• What special position? This is an exercise problem in "Euclidean and non-Euclidean geometry" and there is no such mention – Ki Yoon Eum Dec 3 '18 at 11:23
• And... I solve it actually using Menelaus' theorem! – Ki Yoon Eum Dec 3 '18 at 12:23
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 $$P$$.