MathDB

2

Part of 2004 Iran MO (3rd Round)

Problems(1)

Beautiful

Source: Iran

9/14/2004
AA is a compact convex set in plane. Prove that there exists a point O∈AO \in A, such that for every line XX′XX' passing through OO, where XX and X′X' are boundary points of AA, then 12≤OXOX′≤2. \frac12 \leq \frac {OX}{OX'} \leq 2.
geometrygeometric transformationhomothetyratiocombinatorics proposedcombinatorics