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 AP2=mn, where m and n are relatively prime positive integers. Find m+n.
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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.
DPatrick 9:17:57 pm
 

Revision as of 22:20, 29 March 2014

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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