KöMaL problem A, 2018

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Circle $\omega$ lies in the interior of circle $\Omega$ , on which a point $X$ moves. The tangents from $X$ to $\omega$ intersect $\Omega$ for the second time at points $A\ne X$ and $B\ne X$ . Prove that the lines $AB$ are either all tangent to a fixed circle, or they all pass through a point.

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