A convex pentagon ABCDE satisfies that the sidelengths and AC,AD≤3. Let us choose 2011 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 403 points out of the 2011 given points.
{Edited}
{I posted it correctly before but because of a little confusion deleted the sidelength part, sorry.} trigonometryceiling functioncombinatorics proposedcombinatorics