PUMaC 2024 · 几何（A 组） · 第 2 题

PUMaC 2024 — Geometry (Division A) — Problem 2

Let ABCD be a square of side length 1 made of paper. Let M be the midpoint of side AB . Let E be a point on side BC and let F be a point on side AD such that A lands on line M E when △ AM F is folded across line M F and such that B lands on line M F when △ BM E is folded across line M E . The area of the resulting shape when both folds are made can be √ a − b written as for positive integers a, b, c with b squarefree. Find a + b + c . c ◦

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