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Given points O and A in the plane. Every point in the plane is colored with one of a finite number of colors. Given a point X in the plane, the circle C(X) has center O and radius OX+{\angle AOX\over OX}, where \angle AOX is measured in radians in the range [0,2\pi). Prove that we can find a point X, not on OA, such that its color appears on the circumference of the circle C(X).

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