From the meaning of the question, we can know that circle C is the circumscribed circle of right triangle OAB. Therefore, the center of the circle C is the midpoint of AB.

Because the circumferential angle of the same side opposite to the same chord is equal. So let's assume that OM is parallel to AB.

C is the midpoint of AB, connecting CM and co.

Then CB=CM and the angle MBA= 180- 120=60 degrees.

So we can see that triangle CBM, triangle COM and triangle COA are equilateral triangles.

Therefore, the radius of the circle =CO=OA=3.