There are n>1 distinct points marked in the plane. Prove that there exists a set of circles C such that[color=#FFFFFF]___∙ Each circle in C has unit radius.
[color=#FFFFFF]___∙ Every marked point lies in the (strict) interior of some circle in C.
[color=#FFFFFF]___∙ There are less than 0.3n pairs of circles in C that intersect in exactly 2 points.Note: Weaker results with 0.3n replaced by cn may be awarded points depending on the value of the constant c>0.3.Proposed by Siddharth Choppara, Archit Manas, Ananda Bhaduri, Manu Param combinatoricsgeometrylmaocombinatorial geometry