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PAMO 2023 Problem 1

Source: 2023 Pan African Mathematics Olympaid, Problem 1

May 17, 2023
PAMOgeometry

Problem Statement

In a triangle ABCABC with AB<ACAB<AC, DD is a point on segment ACAC such that BD=CDBD = CD. A line parallel to BDBD meets segment BCBC at EE and line ABAB at FF. Point GG is the intersection of AEAE and BDBD. Show that ∠BCG=∠BCF\angle BCG = \angle BCF. (Côte d’Ivoire)
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