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circumcircle of CGE tangent to AF wanted, internal tangent circles

Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p5

April 18, 2022
tangent circlestangentgeometry

Problem Statement

Circle ω\omega is tangent to the interior of the circle Ω\Omega at the point C. Chord ABAB of circle Ω\Omega is tangent to ω\omega. Chords CFCF and BGBG of circle Ω\Omega intersect at point EE lying on ω\omega. Prove that the circumcircle of triangle CGECGE is tangent to straight line AFAF.
(I. Kukharchuk)
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