# Difference between revisions of "2014 AIME II Problems/Problem 14"

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− | 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 <math>AP^2=m/n</math>, where m and n are relatively prime positive integers. Find m+n. | + | 14. In <math>△ABC, AB=10, ∠A=30∘</math>, and <math>∠C=45∘</math>. 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 <math>AP^2=m/n</math>, where m and n are relatively prime positive integers. Find m+n. |

## Revision as of 22:20, 29 March 2014

14. In $△ABC, AB=10, ∠A=30∘$ (Error compiling LaTeX. ! Package inputenc Error: Unicode char \u8:△ not set up for use with LaTeX.), and $∠C=45∘$ (Error compiling LaTeX. ! Package inputenc Error: Unicode char \u8:∠ not set up for use with LaTeX.). 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 , where m and n are relatively prime positive integers. Find m+n.