PUMaC 2021 · 个人决赛（B 组） · 第 3 题

PUMaC 2021 — Individual Finals (Division B) — Problem 3

Let ∆ ABC be a triangle, and let C , B be the feet of perpendiculars from C and B onto AB 0 0 and AC respectively. Let Γ be the circumcircle of ∆ ABC . Let E be a point on the Γ such that AE ⊥ BC . Let M be the midpoint of BC and let G be the second intersection of EM and Γ. Let T be a point on Γ such that T G is parallel to BC . Prove that T, A, B , C are 0 0 concyclic. 1

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