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equal angles wanted, intersecting circles (2012 Kyiv City MO 8.3)

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August 1, 2020
geometry

Problem Statement

On the circle γ\gamma the points AA and BB are selected. The circle ω\omega touches the segment ABAB at the point KK and intersects the circle γ\gamma at the points MM and NN. The points lie on the circle γ\gamma in the following order: A,  M,  N,  BA, \, \, M, \, \, N, \, \, B. Prove that ∠AMK=∠KNB\angle AMK = \angle KNB.
(Yuri Biletsky)
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