MathDB

G3

Part of 2018 Balkan MO Shortlist

Problems(1)

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

Source: BMO Shortlist 2018 G3

5/5/2019
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
geometrygeometric inequalityinequalitiessemiperimetermaximum valueminimum