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min k such that PQ <= k (BP + QC) , angle trisectors related

Source: 2018 (-19) Swedish Mathematical Competition p5

August 10, 2020
geometrygeometric inequalitytrisector

Problem Statement

In a triangle ABCABC, two lines are drawn that together trisect the angle at AA. These intersect the side BCBC at points PP and QQ so that PP is closer to BB and QQ is closer to CC. Determine the smallest constant kk such that ∣PQ∣≤k(∣BP∣+∣QC∣)| P Q | \le k (| BP | + | QC |), for all such triangles. Determine if there are triangles for which equality applies.
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