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HMMT 二月 2025 · 冲刺赛 · 第 5 题

HMMT February 2025 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [6] Compute the largest possible radius of a circle contained in the region defined by | x + | y || ≤ 1 in the coordinate plane.
解析
  1. [6] Compute the largest possible radius of a circle contained in the region defined by | x + | y || ≤ 1 in the coordinate plane. Proposed by: Rishabh Das √ √ Answer: 2 2 − 2 = 2( 2 − 1) Solution: 1 − 1 After drawing the graph, it’s clear that the circle should pass through ( − 1 , 0) and be tangent to √ √ y = x − 1 and y = − x + 1. Letting the radius of this circle be r , we have r 2 + r = 2, so r = 2 2 − 2 .