# Points on Parallel Chords

Geometry Level 3

$$\Gamma$$ is a circle with center $$O$$. $$AB$$ and $$CD$$ are 2 parallel chords of $$\Gamma$$ such that $$AB = 182$$ and $$CD = 120$$. $$E$$ and $$F$$ are points on $$AB$$ and $$CD$$, respectively, such that $$\angle OEA = \angle OFC = 90^\circ$$. If $$E$$ lies between $$O$$ and $$F$$ and the radius of $$\Gamma$$ is $$109$$, what is the length of $$EF$$?

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