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intersecting circles & tangents at the common, inequality of segments wanted

Source: Sharygin Geometry Olympiad 2015 Final 9.1

August 1, 2018
inequalitiesgeometrytangent circles

Problem Statement

Circles α\alpha and β\beta pass through point CC. The tangent to α\alpha at this point meets β\beta at point BB, and the tangent to β\beta at CC meets α\alpha at point AA so that AA and BB are distinct from CC and angle ACBACB is obtuse. Line ABAB meets α\alpha and β\beta for the second time at points NN and MM respectively. Prove that 2MN<AB2MN < AB.
(D. Mukhin)
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