MathDB

min and max of f (P) =\frac{PA + PB}{PC + PD}, where ABCD is a square

Source: 2012 Serbia EGMO TST p4

September 17, 2018

geometryminimum valuemaximum value

Problem Statement

Let

ABCD

be a square of the plane

P

. Define the minimum and the maximum the value of the function

f: P \to R

is given by

f (P) =\frac{PA + PB}{PC + PD}