MathDB

Beautiful

Source: Iran

September 14, 2004

geometrygeometric transformationhomothetyratiocombinatorics proposedcombinatorics

Problem Statement

A

is a compact convex set in plane. Prove that there exists a point

O \in A

, such that for every line

XX'

passing through

O

, where

X

and

X'

are boundary points of

A

, then

\frac12 \leq \frac {OX}{OX'} \leq 2.