Lines L_{1}, L_{2}, and L_{3} are parallel
(infographic below) with O and Q on L_{2}. Circles O and Q with radius OQ intersect at A and B. AO
meets L_{3} at C, BO meets L_{1} at D. CE is
parallel to BO (E on L_{1}) and DF is parallel to AO (F
on L_{3}). Prove that triangle OEF is
equilateral.
