HMMT 十一月 2024 · GEN 赛 · 第 2 题
HMMT November 2024 — GEN Round — Problem 2
题目详情
- Let RAN DOM be a regular hexagon with side length 1 . Points I and T lie on segments RA and DO , ◦ respectively, such that M I = M T and ∠ T M I = 90 . Compute the area of triangle M IT . b c c
解析
- Let RAN DOM be a regular hexagon with side length 1. Points I and T lie on segments RA and DO , ◦ respectively, such that M I = M T and ∠ T M I = 90 . Compute the area of triangle M IT . Proposed by: Linus Yifeng Tang 3 Answer: = 0 . 75 4 Solution: I A R N M D T O By symmetry, IT must be perpendicular to RA and DO . Therefore, the length of IT is the height of √ 1 3 2 the hexagon, which is 3. So, the area of triangle M IT is IT = . 4 4 b c c