MathDB

n points on the plane

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 9

May 31, 2009

rotationinequalitiesgeometry proposedgeometry

Problem Statement

Given

n

points on the plane, which are the vertices of a convex polygon,

n > 3

. There exists

k

regular triangles with the side equal to

1

and the vertices at the given points. [*] Prove that

k < \frac {2}{3}n

. [*] Construct the configuration with

k > 0.666n