What is a good way to prove this problem?

Good question! This one was hard, and involved lots of algebraic tinkering. We know that OA=OB=OC. Construct lines AC and OB. The large triangle formed by these constructions is comprised of three isosceles triangles. We know something about isosceles triangles and opposite angles right? That'll give you some additional equalities. Now consider that angles OAC, OCA, OCB, OBC, OBA, and OAB sum to 180. So now you've got a bunch of equalities. Find something relating angle AOC to the angles about which you already have information. All you've got to do is use all the equalities you've got to relate AOC with ABC, and the answer will come out. Good luck!

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