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ABC isosceles wanted, BG > BF = GC 2007 Cuba MO 2.6

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September 15, 2024
geometryisosceles

Problem Statement

Let the triangle ABCABC be acute. Let us take in the segment BCBC two points FF and GG such that BG>BF=GCBG > BF = GC and an interior pointP P to the triangle on the bisector of ∠BAC\angle BAC. Then are drawn through PP, PD∥ABPD\parallel AB and PE∥ACPE \parallel AC, D∈ACD \in AC and E∈ABE \in AB, ∠FEP=∠PDG\angle FEP = \angle PDG. prove that △ABC\vartriangle ABC is isosceles.
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