HMMT 二月 2005 · 冲刺赛 · 第 23 题
HMMT February 2005 — Guts Round — Problem 23
题目详情
- [9] The sides of a regular hexagon are trisected, resulting in 18 points, including ver- tices. These points, starting with a vertex, are numbered clockwise as A , A , . . . , A . 1 2 18 The line segment A A is drawn for k = 1 , 4 , 7 , 10 , 13 , 16, where indices are taken k k +4 modulo 18. These segments define a region containing the center of the hexagon. Find the ratio of the area of this region to the area of the large hexagon.
解析
- The sides of a regular hexagon are trisected, resulting in 18 points, including vertices. These points, starting with a vertex, are numbered clockwise as A , A , . . . , A . The 1 2 18 line segment A A is drawn for k = 1 , 4 , 7 , 10 , 13 , 16, where indices are taken modulo k k +4