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Consider a circle with center O and radius R, and let A and B be two points in the plane of this circle.

a.) Draw a chord CD of the circle such that CD is parallel to AB, and the point of the intersection P of the lines AC and BD lies on the circle.

b.) Show that generally, one gets two possible points P (P_{1} and P_{2}) satisfying the condition of the above problem, and compute the distance between these two points, if the lengths OA=a, OB=b and AB=d are given.

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