4th Centromerican 2002 Problem B1 ABC is a triangle. D is the midpoint of BC. E is a point on the side AC such that BE = 2AD. BE and AD meet at F and ∠FAE = 60 o . Find ∠FEA.
Thanks to José Nelson Ramirez Let the line parallel to BE through D meet AC at G. Then DCG, BCE are similar and BC = 2 DC, so BE = 2 DG. Hence AD = DG, so ∠DGA = ∠DAG = 60 o . FE is parallel to DG, so ∠FEA = 60 o . 4th OMCC 2002 © John Scholes jscholes@kalva.demon.co.uk 26 November 2003 Last corrected/updated 26 Nov 03