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Concyclic with a Tangent Circle

Source: KJMO 2022 P6

October 29, 2022
geometrycircumcircleConcyclictangent

Problem Statement

Let ABCABC be a isosceles triangle with AB‾=AC‾\overline{AB}=\overline{AC}. Let D(≠A,C)D(\neq A, C) be a point on the side ACAC, and circle Ω\Omega is tangent to BDBD at point EE, and ACAC at point CC. Denote by F(≠E)F(\neq E) the intersection of the line AEAE and the circle Ω\Omega, and G(≠a)G(\neq a) the intersection of the line ACAC and the circumcircle of the triangle ABFABF. Prove that points D,E,F,D, E, F, and GG are concyclic.
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