HMMT 二月 2005 · 冲刺赛 · 第 12 题
HMMT February 2005 — Guts Round — Problem 12
题目详情
- [7] Two vertices of a cube are given in space. The locus of points that could be a third vertex of the cube is the union of n circles. Find n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 19, 2005 — GUTS ROUND √ √
解析
- Two vertices of a cube are given in space. The locus of points that could be a third vertex of the cube is the union of n circles. Find n . Solution: 10 Let the distance between the two given vertices be 1. If the two given vertices are adjacent, then the other vertices lie on four circles, two of radius 1 and two of radius √