PUMaC 2021 · 几何（A 组） · 第 8 题

PUMaC 2021 — Geometry (Division A) — Problem 8

Let ABC be an acute triangle with side lengths AB = 7 , BC = 12 , AC = 10, and let ω be its incircle. If ω is touching AB, AC at F, E , respectively, and if EF intersects BC at X , suppose that the ratio in which the angle bisector of ∠ BAC divides the segment connecting midpoint a of EX and C is , where a, b are relatively prime integers. Find a + b. b 1

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