HMMT 二月 2004 · 冲刺赛 · 第 15 题
HMMT February 2004 — Guts Round — Problem 15
题目详情
- [7] A regular decagon A A A · · · A is given in the plane. Compute ∠ A A A in 0 1 2 9 0 3 7 degrees. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND
解析
- A regular decagon A A A · · · A is given in the plane. Compute ∠ A A A in degrees. 0 1 2 9 0 3 7 ◦ Solution: 54 ◦ ◦ Put the decagon in a circle. Each side subtends an arc of 360 / 10 = 36 . The in- scribed angle ∠ A A A contains 3 segments, namely A A , A A , A A , so the angle 0 3 7 7 8 8 9 9 0 ◦ ◦ is 108 / 2 = 54 .