PUMaC 2025 · 几何（A 组） · 第 5 题

PUMaC 2025 — Geometry (Division A) — Problem 5

Let ABC be a triangle with ∠ BAC = 60 , AB = 10, AC = 13, and orthocenter H . Let ω 1 be the circle through H tangent to BC at B , and let ω be the circle through H tangent to 2 BC at C . Let CH intersect ω again at U and let BH intersect ω again at V . Let N be the 1 2 N U point on the same side of BC as A such that triangle BN C is equilateral. Find . N V

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