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Mn visible with a constanr angle

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005
geometry proposedgeometry

Problem Statement

A circleΓ\Gamma with radius RR and center ω\omega, and a line dd are drawn on a plane, such that the distance of ω\omega from dd is greater than RR. Two points MM and NN vary on dd so that the circle with diameter MNMN is tangent to Γ\Gamma. Prove that there is a point PP in the plane from which all the segments MNMN are visible at a constant angle.
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