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Prove that the angle $GFC$ and $BAC$ are equal.

Source: Moldova JTST 2023

May 5, 2023
geometrycircumcircleparallelogram

Problem Statement

Let Ω\Omega be the circumscribed circle of the acute triangle ABCABC and D D a point the small arc BCBC of Ω\Omega. Points EE and F F are on the sides AB AB and ACAC, respectively, such that the quadrilateral CDEFCDEF is a parallelogram. Point GG is on the small arc ACAC such that lines DCDC and BGBG are parallel. Prove that the angles GFCGFC and BACBAC are equal.
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