MathDB

Two circles are given for which there is a family of quadrilaterals circumscribed around the first circle and inscribed in the second. Let's denote by

a, b, c

and

d{}

the consecutive lengths of the sides of one of these quadrilaterals. Prove that the sum

\frac{a}{c}+\frac{c}{a}+\frac{b}{d}+\frac{d}{b}

does not depend on the choice of the quadrilateral.
Proposed by I. Weinstein

Problem Statement