Right-Angle Point

Geometry Level 3

\(\Gamma\) is a circle with center \(O\). \(A\) and \(B\) are points on the circumference of \(\Gamma\) and \(C\) is a point within \(\Gamma\) such that \(\angle ACB = 90^\circ\). If \(AC = 8\), \(BC = 6\), and the radius of \(\Gamma\) is \(5\sqrt{5}\), what is the value of \(OC^2\)?

Details and assumptions

Be very careful with how your draw the diagram. Do not make any unwarranted assumptions.

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