Determining the measure of a central angle in a circle ( subject math GRE exam 9768 Q.23).

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The question is given in the following picture:

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I know that the triangle ABC will be an isosceles triangle but I do not know how to use this knowledge in the solution, could anyone help me please ?

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HINT

Let the radius of the two circles to be $r$, then $OA=OB=OC=r=AO=AB=AC$