HMMT 十一月 2014 · THM 赛 · 第 7 题
HMMT November 2014 — THM Round — Problem 7
题目详情
英文原题
- Let P be a parabola with focus F and directrix ℓ . A line through F intersects P at two points A and
B . Let D and C be the feet of the altitudes from A and B onto ℓ , respectively. Given that AB = 20
and CD = 14, compute the area of ABCD .
解析
英文解析
- Let P be a parabola with focus F and directrix ℓ . A line through F intersects P at two points A and
B . Let D and C be the feet of the altitudes from A and B onto ℓ , respectively. Given that AB = 20
and CD = 14, compute the area of ABCD .
Answer: 140 Observe that AD + BC = AF + F B = 20, and that ABCD is a trapezoid withheight BC = 14. Hence the answer is ( AD + BC )(14) = 140.1 2