PUMaC 2021 · 几何（A 组） · 第 4 题

PUMaC 2021 — Geometry (Division A) — Problem 4

Let BCDE be a trapezoid with BE ∥ CD, BE = 20 , BC = 2 34 , CD = 8 , DE = 2 10 . Draw a line through E parallel to BD and a line through B perpendicular to BE, and let A be the intersection of these two lines. Let M be the intersection of diagonals BD and CE, and a let X be the intersection of AM and BE. If BX can be written as , where a, b are relatively b prime positive integers, find a + b.

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