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Min and Max values of PD+PE+PF of cevians

Source: Czech-Polish-Slovak 2002 Q2

April 28, 2013

geometryinequalitiesgeometry unsolved

Problem Statement

A triangle

ABC

has sides

BC = a, CA = b, AB = c

with

a < b < c

and area

S

. Determine the largest number

u

and the least number

v

such that, for every point

P

inside

\triangle ABC

, the inequality

u \le PD + PE + PF \le v

holds, where

D,E, F

are the intersection points of

AP,BP,CP

with the opposite sides.

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