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Largest Area

Source: 1984 National High School Mathematics League, Exam Two, Problem 3

February 22, 2020
geometry

Problem Statement

In △ABC\triangle ABC, PP is a point on BCBC. F∈AB,E∈AC,PF//CA,PE//BAF\in AB,E\in AC,PF//CA,PE//BA. If S△ABC=1S_{\triangle ABC}=1, prove that at least one of S△BPF,S△PCE,SPEAFS_{\triangle BPF},S_{\triangle PCE},S_{PEAF} is not less than 49\frac{4}{9}.
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