MathDB
equal segments wanted, related to an isosceles triangle and 2 circumcircles

Source: INAMO Shortlist 2015 G4

May 14, 2019
geometryequal segmentsisoscelescircumcircle

Problem Statement

Given an isosceles triangle ABCABC with AB=ACAB = AC, suppose DD is the midpoint of the ACAC. The circumcircle of the DBCDBC triangle intersects the altitude from AA at point EE inside the triangle ABCABC, and the circumcircle of the triangle AEBAEB cuts the side BDBD at point FF. If CFCF cuts AEAE at point GG, prove that AE=EGAE = EG.