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tangent wanted, isosceles, 3 circles, tangents given

Source: Ukrainian Geometry Olympiad 2020, XI p2

April 27, 2020
geometrytangent circlesisoscelestangent

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB=AC. Circle Γ\Gamma lies outside ABCABC and touches line ACAC at point CC. The point DD is chosen on circle Γ\Gamma such that the circumscribed circle of the triangle ABDABD touches externally circle Γ\Gamma. The segment ADAD intersects circle Γ\Gamma at a point EE other than DD. Prove that BEBE is tangent to circle Γ\Gamma .
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