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Geometry Problem 980. Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Construction

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Lines L1, L2, and L3 are parallel (infographic below) with O and Q on L2. Circles O and Q with radius OQ intersect at A and B. AO meets L3 at C, BO meets L1 at D. CE is parallel to BO (E on L1) and DF is parallel to AO (F on L3). Prove that triangle OEF is equilateral.
 

Geometry Problem 980: Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Construction

 

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