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tangent circles inside a parallelogram (2011 Kyiv City MO 11.4.1)

Source:

July 15, 2020
geometryparallelogramcirclestangent

Problem Statement

Inside the parallelogram ABCDABCD are the circles γ1\gamma_1 and γ2\gamma_2, which are externally tangent at the point KK. The circle γ1\gamma_1 touches the sides ADAD and ABAB of the parallelogram, and the circle γ2\gamma_2 touches the sides CDCD and CBCB. Prove that the point KK lies on the diagonal ACAC of the paralelogram.
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