Very beautiful problem
Source: Iran selction test 2002
April 3, 2004
geometry3D geometrysphereinequalitiesgeometry unsolved
Problem Statement
A "2-line" is the area between two parallel lines. Length of "2-line" is distance of two parallel lines. We have covered unit circle with some "2-lines". Prove sum of lengths of "2-lines" is at least 2.