I am encountering 2 questions from my professor. Can anybody help me?? I really have no idea about them. Thx!
1. The incircle of triangle ABC touch sides AB,BC, CA at M,N,K, respectively. The line through A parallel to NK meets MN at D. The line through A parallel to MN meets NK at E. Show that the line DE bisects sides AB and AC of triangle ABC.
2. In triangle ABC, AB = AC and the angle bisector of C meets AB at D. The perpendicular to CD through the center of the circumcircle of ABC intersects BC at E. The parallel to CD through E meets AB at F. Show that BE = FD.