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circle tangent to incircle, <BKA=45^o (2021 Kyiv City MO Round2 11.3)

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February 15, 2021
geometrytangent circles

Problem Statement

In the triangle ABCABC, the altitude BHBH and the angle bisector BLBL are drawn, the inscribed circle ww touches the side of the ACAC at the point KK. It is known that ∠BKA=45o\angle BKA = 45^o. Prove that the circle with diameter HLHL touches the circle ww.
(Anton Trygub)
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