HMMT 二月 2015 · 几何 · 第 6 题
HMMT February 2015 — Geometry — Problem 6
题目详情
英文原题
- In triangle ABC , AB = 2, AC = 1 + 5, and ∠ CAB = 54 . Suppose D lies on the extension of AC
√
through C such that CD = 5 − 1. If M is the midpoint of BD , determine the measure of ∠ ACM ,
in degrees. 1
解析
英文解析
- In triangle ABC , AB = 2, AC = 1 + 5, and ∠ CAB = 54 . Suppose D lies on the extension of AC
√
through C such that CD = 5 − 1. If M is the midpoint of BD , determine the measure of ∠ ACM ,
in degrees.
√ √
Answer: 63 Let E be the midpoint of AD . EC = 5 + 1 − 5 = 1, and EM = 1 by similar
°
triangles ( ABD ∼ EM D ). △ ECM is isosceles, with m ∠ CEM = 54 . Thus m ∠ ACM = m ∠ ECM =
180 − 54 °
= 63 .
12