PUMaC 2021 · 几何（A 组） · 第 7 题

PUMaC 2021 — Geometry (Division A) — Problem 7

Let ABC be a triangle with side lengths AB = 13 , AC = 17 , and BC = 20 . Let E, F be the feet of the altitudes from B onto AC and C onto AB, respectively. Let P be the second √ a b intersection of the circumcircles of ABC and AEF. Suppose that AP can be written as c where a, c are relatively prime and b is square-free. Compute a.

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