2020 CIME I Problems/Problem 14
Problem 14
Let be a triangle with sides . Denote by and the circumcenter and incenter of , respectively. The incircle of touches at , and line intersects the circumcircle of again at . Then the length of can be expressed in the form , where are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find .
Solution
Analytic geometry gives us The answer is .
See also
2020 CIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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