2014 AIME II Problems/Problem 14

14. In △ABC, AB=10, ∠A=30∘, and ∠C=45∘. Let H, D, and M be points on the line BC¯¯¯¯¯ such that AH¯¯¯¯¯¯⊥BC¯¯¯¯¯, ∠BAD=∠CAD, and BM=CM. Point N is the midpoint of the segment HM¯¯¯¯¯¯¯, and point P is on ray AD such that PN¯¯¯¯¯¯⊥BC¯¯¯¯¯. Then AP2=mn, where m and n are relatively prime positive integers. Find m+n. DPatrick 9:17:57 pm