HMMT 十一月 2025 · 冲刺赛 · 第 20 题

HMMT November 2025 — Guts Round — Problem 20

[11] Suppose that ABCD and AXY Z are squares with side lengths 10 and 7, respectively. Given that X lies inside triangle ABY and Y lies on segment BD , compute the area of triangle BXC .

解析

[11] Suppose that ABCD and AXY Z are squares with side lengths 10 and 7, respectively. Given that X lies inside triangle ABY and Y lies on segment BD , compute the area of triangle BXC . Proposed by: Pitchayut Saengrungkongka Answer: 25 Solution: Z A D Y X B C © 2025 HMMT ◦ ◦ Since ∠ ABY = 45 and ∠ AXY = 90 , we get that X is the circumcenter of triangle ABY . Therefore, 1 XA = XB , so X lies on the midsegment between AD and BC . Hence, the answer is · 10 · 5 = 25 . 2