HMMT 十一月 2018 · THM 赛 · 第 3 题
HMMT November 2018 — THM Round — Problem 3
题目详情
- HOW , BOW , and DAH are equilateral triangles in a plane such that W O = 7 and AH = 2. Given that D, A, B are collinear in that order, find the length of BA .
解析
- HOW , BOW , and DAH are equilateral triangles in a plane such that W O = 7 and AH = 2. Given that D, A, B are collinear in that order, find the length of BA . Proposed by: James Lin Answer: 11 Note that H 6 = B since otherwise DAB is an equilateral triangle. Let M be the midpoint of DA , so √ √ ◦ HB = 7 3 and HM = 3, and ∠ HM B = 90 . By the Pythagorean theorem, √ √ √ 2 2 BM = (7 3) − ( 3) = 12 . Then BA = BM − AM = 11.