Two circles centered at points O1 and O2, intersect at points A and B. Prove that angle O1 A O2 = angle O1 B O2.

Consider triangles OO1A and OO1B.

The side OO1 of the triangles is common, O1A = O1B as the radii of one circle, OA = OB as the radii of the second circle, then the triangles OO1A is equal to the triangle OO1B, and then the angle OO1A = OO1B, which was required to be proved.



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