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Tangent circles in non-standart configuration

Source: Latvian TST for Baltic Way 2019, Problem 12

June 4, 2020
geometryperimetergeometric transformationreflectioncircumcircle

Problem Statement

Let AXAX, AYAY be tangents to circle ω\omega from point AA. Le BB, CC be points inside AXAX and AYAY respectively, such that perimeter of △ABC\triangle ABC is equal to length of AXAX. DD is reflection of AA over BCBC. Prove that circumcircle △BDC\triangle BDC and ω\omega are tangent to each other.
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