Let triangle ABC be such that AB is not congruent to AC. Let D be the point of intersection of the bisector of angle A and the perpendicular bisector of side BC. Let E, F, and G be the feet of the perpendicular dropped from D to line AB, line AC, line BC.
(I drew the figure but I don't know how to start up the following proofs)
a) D lies outside the triangle on the circle through ABC.
b) One of E or F lies inside the triangle and the other outside.
c) E, F, and G are collinear.