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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