2002 AIME II Problems/Problem 14
Problem
The perimeter of triangle is , and the angle is a right angle. A circle of radius with center on is drawn so that it is tangent to and . Given that where and are relatively prime positive integers, find .
Solution
Let the circle intersect at . Then note and are similar. Also note that by power of a point. So we have Solving, . So the ratio of the side lengths of the triangles is 2. Therefore, so and Substituting for , we see that , so and the answer is .
See also
2002 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AIME Problems and Solutions |