PUMaC 2025 · 个人决赛（A 组） · 第 3 题

PUMaC 2025 — Individual Finals (Division A) — Problem 3

Let ABC be an acute scalene triangle with orthocenter H , circumcenter O and circumcircle Ω. It is given that OH ∥ BC . Line OH meets side AB at U and side AC at V . Let R be on ◦ Ω such that ∠ ARH = 90 . Let the circumcircle of triangle ROH meet Ω a second time at S . Show that lines SO and RH meet on the circumcircle of triangle RU V . 1

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