MathDB

6

Part of 2019 Canadian Mathematical Olympiad Qualification

Problems(1)

4 lines concurrent means 5 lines concur, pentagon and perpendiculars

Source: Canada Repêchage 2019/6 CMOQR

3/1/2020
Pentagon ABCDEABCDE is given in the plane. Let the perpendicular from AA to line CDCD be FF, the perpendicular from BB to DEDE be GG, from CC to EAEA be HH, from DD to ABAB be II,and from EE to BCBC be JJ. Given that lines AF,BG,CHAF,BG,CH, and DIDI concur, show that they also concur with line EJEJ.
pentagonconcurrentconcurrencygeometryperpendicular