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Italian Mathematical Olympiad 2022 - Problem 2

Source:

May 6, 2022
geometry

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB<AC. Let then • DD be the foot of the bisector of the angle in AA, • EE be the point on segment BCBC (different from BB) such that AB=AEAB=AE, • FF be the point on segment BCBC (different from BB) such that BD=DFBD=DF, • GG be the point on segment ACAC such that AB=AGAB=AG. Prove that the circumcircle of triangle EFGEFG is tangent to line ACAC.
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