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Nice geometry problem about incenter

Source: 1st TASIMO, Day1 Problem1

May 18, 2024
geometryincenter

Problem Statement

Let ABCABC be a triangle with AB<ACAB<AC and incenter I.I. A point DD lies on segment ACAC such that AB=AD,AB=AD, and the line BIBI intersects ACAC at E.E. Suppose the line CICI intersects BDBD at F,F, and GG lies on segment DIDI such that FD=FG.FD=FG. Prove that the lines AGAG and EFEF intersect on the circumcircle of triangle CEI.CEI. \\ Proposed by Avan Lim Zenn Ee, Malaysia
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