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Trisecting a chord

Source: China Second Round (A) 2013 Q1

May 15, 2016
geometry

Problem Statement

ABAB is a chord of circle ω\omega, PP is a point on minor arc ABAB, E,FE,F are on segment ABAB such that AE=EF=FBAE=EF=FB. PE,PFPE,PF meets ω\omega at C,DC,D respectively. Prove that EF⋅CD=AC⋅BDEF\cdot CD=AC\cdot BD.
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