HMMT 二月 2008 · GEN2 赛 · 第 8 题
HMMT February 2008 — GEN2 Round — Problem 8
题目详情
英文原题
- [ 5 ] A piece of paper is folded in half. A second fold is made such that the angle marked below has
° °
measure φ (0 < φ < 90 ), and a cut is made as shown below.
When the piece of paper is unfolded, the resulting hole is a polygon. Let O be one of its vertices.Á
°
Suppose that all the other vertices of the hole lie on a circle centered at O , and also that ∠ XOY = 144 ,
where X and Y are the the vertices of the hole adjacent to O . Find the value(s) of φ (in degrees).
解析
英文解析
- [ 5 ] A piece of paper is folded in half. A second fold is made such that the angle marked below has
° °
measure φ (0 < φ < 90 ), and a cut is made as shown below.
Á1
When the piece of paper is unfolded, the resulting hole is a polygon. Let O be one of its vertices.
°
Suppose that all the other vertices of the hole lie on a circle centered at O , and also that ∠ XOY = 144 ,
where X and Y are the the vertices of the hole adjacent to O . Find the value(s) of φ (in degrees).
°
Answer: 81 Same as Geometry Test problem 5.