PUMaC 2017 · 几何（B 组） · 第 6 题
PUMaC 2017 — Geometry (Division B) — Problem 6
题目详情
- An equilateral triangle ABC has side length 7. Point P is in the interior of triangle ABC , such that P B = 3 and P C = 5. The distance between the circumcenters of ABC and P BC √ m n can be expressed as , where n not divisible by the square of any prime and m and p are p relatively prime positive integers. What is m + n + p ?
解析
- Note that ∠ BP C = 180 − ∠ A . Thus, if we reflect P over BC to P , P lies on the circumcircle of ABC . This means that the circumcircles of ABC and P BC are congruent. Their radius is √ √ 7 3 7 3 , so the distance between their circumcenters is . Thus, m + n + p = 13 . 3 3 Problem written by Kai Zheng