PUMaC 2025 · 几何（B 组） · 第 8 题

PUMaC 2025 — Geometry (Division B) — Problem 8

Let ABC be a triangle with AB = 7, BC = 6 and AC = 8. Let M be the midpoint of BC M S 1 and let S be on segment AM such that = . The line through A parallel to BC meets AM 4 the circumcircles of triangles ASB and ASC at D ̸ = A and E ̸ = A , respectively. Find DE . Remark. Regrettably, due to an error on behalf of the author, the in-contest problem statement M S M S 1 had the ratio written as = 4 instead of = . AM AM 4 1

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