Difference between revisions of "2014 AIME I Problems/Problem 15"
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== Problem 15 == | == Problem 15 == | ||
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| + | In \triangle ABC, AB = 3, BC = 4, and CA = 5. Circle \omega intersects \overline{AB} at E and B, \overline{BC} at B and D, and \overline{AC} at F and G. Given that EF=DF and \frac{DG}{EG} = \frac{3}{4}, length DE=\frac{a\sqrt{b}}{c}, where a and c are relatively prime positive integers, and b is a positive integer not divisible by the square of any prime. Find a+b+c. | ||
== Solution == | == Solution == | ||
Revision as of 10:40, 14 March 2014
Problem 15
In \triangle ABC, AB = 3, BC = 4, and CA = 5. Circle \omega intersects \overline{AB} at E and B, \overline{BC} at B and D, and \overline{AC} at F and G. Given that EF=DF and \frac{DG}{EG} = \frac{3}{4}, length DE=\frac{a\sqrt{b}}{c}, where a and c are relatively prime positive integers, and b is a positive integer not divisible by the square of any prime. Find a+b+c.
