Difference between revisions of "2014 AIME II Problems/Problem 14"
(Created page with "14. In △ABC, AB=10, ∠A=30∘, and ∠C=45∘. Let H, D, and M be points on the line <math><math>\overline{BC}</math></math> such that <math><math>\overline{AH}⊥</math>\over...") |
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| − | 14. In △ABC, AB=10, ∠A=30∘, and ∠C=45∘. Let H, D, and M be points on the line | + | 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 | ||
Revision as of 21:18, 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 AP2=mn, where m and n are relatively prime positive integers. Find m+n. DPatrick 9:17:57 pm
