HMMT 二月 2024 · 冲刺赛 · 第 4 题
HMMT February 2024 — Guts Round — Problem 4
题目详情
- [5] Equilateral triangles ABF and BCG are constructed outside regular pentagon ABCDE . Compute ∠ F EG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT February 2024, February 17, 2024 — GUTS ROUND Organization Team Team ID#
解析
- [5] Equilateral triangles ABF and BCG are constructed outside regular pentagon ABCDE . Compute ∠ F EG . Proposed by: Karthik Venkata Vedula 4 π ◦ Answer: 48 = 15 ◦ Solution: We have ∠ F EG = ∠ AEG − ∠ AEF . Since EG bisects ∠ AED , we get ∠ AEG = 54 . ◦ ◦ ◦ ◦ Now, ∠ EAF = 108 + 60 = 168 . Since triangle EAF is isosceles, this means ∠ AEF = 6 , so the ◦ ◦ ◦ answer is 54 − 6 = 48 . G F B C A D E