HMMT 二月 2008 · GEN2 赛 · 第 8 题
HMMT February 2008 — GEN2 Round — Problem 8
题目详情
- [ 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. Á 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).
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. 1 Á 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.