There exists a unit circle - [VMO 2011]
Source:
January 11, 2011
trigonometryceiling functioncombinatorics proposedcombinatorics
Problem Statement
A convex pentagon satisfies that the sidelengths and Let us choose distinct points inside this pentagon. Prove that there exists an unit circle with centre on one edge of the pentagon, and which contains at least points out of the given points.
{Edited}
{I posted it correctly before but because of a little confusion deleted the sidelength part, sorry.}