2

Part of 2002 Czech-Polish-Slovak Match

Problems(1)

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

Source: Czech-Polish-Slovak 2002 Q2

ABC

BC = a, CA = b, AB = c

u \le PD + PE + PF \le v

S

. Determine the largest number

u

and the least number

v

such that, for every point

P

\triangle ABC

, the inequality

u \le PD + PE + PF \le v

D,E, F

are the intersection points of

AP,BP,CP

with the opposite sides.

geometryinequalitiesgeometry unsolved