2014 AIME II Problems/Problem 14

Revision as of 22:20, 29 March 2014 by Gamjawon (talk | contribs)

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 $AP^2=m/n$, where m and n are relatively prime positive integers. Find m+n.

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