MathDB

Let

a

and

b

be positive real numbers with

a\ge b

. Let

\rho

be the maximum possible value of

\frac{a}{b}

for which the system of equations a^2\plus{}y^2\equal{}b^2\plus{}x^2\equal{}(a\minus{}x)^2\plus{}(b\minus{}y)^2has a solution in

(x,y)

satisfying

0\le x<a

and

0\le y<b

. Then

\rho^2

can be expressed as a fraction

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find m\plus{}n.

Problem Statement