ToT 2022-spring SO5
A quadrilateral ABCD is inscribed into a circle ω with center O. The circumcircle of the triangle AOC intersects the lines AB, BC, CD and DA the second time at the points M, N, K and L respectively. Prove that the lines MN, KL and the tangents to ω at the points A and C all touch the same circle.
Dataset text AI-MO AoPS. Quoted with source.
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