HMMT 二月 2004 · 几何 · 第 6 题
HMMT February 2004 — Geometry — Problem 6
题目详情
英文原题
- In trapezoid ABCD shown, AD is parallel to BC , and AB = 6 , BC = 7 , CD =
8 , AD = 17. If sides AB and CD are extended to meet at E , find the resulting angleat E (in degrees).
B 7 CE
D68
17A
解析
英文解析
- In trapezoid ABCD shown, AD is parallel to BC , and AB = 6 , BC = 7 , CD =
8 , AD = 17. If sides AB and CD are extended to meet at E , find the resulting angleat E (in degrees).
Solution: 90
Choose point F on AD so that BCDF is a parallelogram. Then BF = CD = 8, and
AF = AD − DF = AD − BC = 10, so 4 ABF is a 6-8-10 right triangle. The required
°
angle is equal to ABF = 90 .6
B 7 C2
6 88
10AD
F 7