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HMMT 二月 2004 · 冲刺赛 · 第 15 题

HMMT February 2004 — Guts Round — Problem 15

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [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.
    HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND

英文原题

[7] A regular decagon A 0 A 1 A 2 · · · A 9 is given in the plane. Compute ∠ A 0 A 3 A 7 in
degrees.
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND

解析

英文解析

  1. 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 inscribed 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 .