HMMT 十一月 2023 · 冲刺赛 · 第 20 题

HMMT November 2023 — Guts Round — Problem 20

[11] Let ABCD be a square of side length 10. Point E is on ray AB such that AE = 17, and point F − − → is on ray AD such that AF = 14. The line through B parallel to CE and the line through D parallel to CF meet at P . Compute the area of quadrilateral AEP F .

解析

[11] Let ABCD be a square of side length 10. Point E is on ray AB such that AE = 17, and point F − − → is on ray AD such that AF = 14. The line through B parallel to CE and the line through D parallel to CF meet at P . Compute the area of quadrilateral AEP F . Proposed by: Pitchayut Saengrungkongka Answer: 100 Solution: E 7 C B 10 P A 10 4 D F From BP ∥ CE , we get that [ BP E ] = [ BP C ]. From DP ∥ CF , we get that [ DP F ] = [ DP C ]. Thus, [ AEP F ] = [ BACP ] + [ BP E ] + [ DP F ] = [ BACP ] + [ BP C ] + [ DP C ] = [ ABCD ] 2 = 10 = 100 .