Distance from the Center

Geometry Level 5

Circle \( \Gamma\) with center \(O\) has diameter \(AB = 192 \). \(C\) is a point outside of \(\Gamma\), such that \(D\) is the foot of the perpendicular from \(C\) to \(AB\) and \(D\) lies on the line segment \(OB\). From \(C\), a tangent to \(\Gamma\) is drawn, touching \(\Gamma\) at \(E\), where the foot of the perpendicular from \(E\) to \(AB\) lies within \(AD\). \(CD\) intersects \(EB\) at \(F\). If \(CF = 110\), what is the length of \(OC\)?

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