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max of \min (\frac{PA}{p-a},\frac{PB}{p-b},\frac{PC}{p-c} ).

Source: BMO Shortlist 2018 G3

May 5, 2019
geometrygeometric inequalityinequalitiessemiperimetermaximum valueminimum

Problem Statement

Let PP be an interior point of triangle ABCABC. Let a,b,ca,b,c be the sidelengths of triangle ABCABC and let pp be it's semiperimeter. Find the maximum possible value of min⁡(PAp−a,PBp−b,PCp−c) \min\left(\frac{PA}{p-a},\frac{PB}{p-b},\frac{PC}{p-c}\right) taking into consideration all possible choices of triangle ABCABC and of point PP.
by Elton Bojaxhiu, Albania
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