Right-Angle Point

Geometry Level 3

Γ\Gamma is a circle with center OO. AA and BB are points on the circumference of Γ\Gamma and CC is a point within Γ\Gamma such that ACB=90\angle ACB = 90^\circ. If AC=8AC = 8, BC=6BC = 6, and the radius of Γ\Gamma is 555\sqrt{5}, what is the value of OC2OC^2?

Details and assumptions

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

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