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Tangents from a point varied on a circle

Source: KöMaL A. 733

November 12, 2018
geometry

Problem Statement

Circle ω\omega lies in the interior of circle Ω\Omega, on which a point XX moves. The tangents from XX to ω\omega intersect Ω\Omega for the second time at points A≠XA\neq X and B≠XB\neq X. Prove that the lines ABAB are either all tangent to a fixed circle, or they all pass through a point.
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