HMMT 十一月 2021 · 团队赛 · 第 1 题
HMMT November 2021 — Team Round — Problem 1
题目详情
- [20] Let ABCD be a parallelogram. Let E be the midpoint of AB and F be the midpoint of CD . Points P and Q are on segments EF and CF , respectively, such that A , P , and Q are collinear. Given that EP = 5, P F = 3, and QF = 12, find CQ .
解析
- [20] Let ABCD be a parallelogram. Let E be the midpoint of AB and F be the midpoint of CD . Points P and Q are on segments EF and CF , respectively, such that A , P , and Q are collinear. Given that EP = 5, P F = 3, and QF = 12, find CQ . Proposed by: Daniel Zhu Answer: 8 Solution: Q F D C P A B E P E 5 Triangles P F Q and P EA are similar, so AE = F Q · = 12 · = 20. Now, CQ = CF − QF = P F 3 20 − 12 = 8.