2011 AIME II Problems/Problem 4
In triangle ABC, AB=(20/11)AC. The angle bisector of angle A intersects BC at point D, and point M is the midpoint of AD. Let P be the point of intersection of AC and the line BM. The ratio of CP to PA can be expresses in the form m/n, where m and n are relatively prime positive integers. Find m+n.
I have no idea, but can be solved with relatively simple geometry. (I ran out of time to solve this one)