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2 circles passing through parallel chords of parabola

Source: 2011 Belarus TST 6.1

June 14, 2020
conicsparabolacirclesChordsparallelgeometry

Problem Statement

ABAB and CDCD are two parallel chords of a parabola. Circle S1S_1 passing through points A,BA,B intersects circle S2S_2 passing through C,DC,D at points E,FE,F. Prove that if EE belongs to the parabola, then FF also belongs to the parabola.
I.Voronovich
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