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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