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HMMT 二月 2008 · 几何 · 第 1 题

HMMT February 2008 — Geometry — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] How many different values can ∠ ABC take, where A , B , C are distinct vertices of a cube?
解析

英文解析

  1. [ 3 ] How many different values can ∠ ABC take, where A , B , C are distinct vertices of a cube?
    √ √ √
    Answer: 5 . In a unit cube, there are 3 types of triangles, with side lengths (1 , 1 , 2), (1 , 2 , 3)
    √ √ √
    and ( 2 , 2 , 2). Together they generate 5 different angle values.