A $4$-isosceles $7$-point Set with Both Circle and Linear Restrictions

Abstract

A finite planar set is $k$-isosceles for $k\ge 3$, if every $k$-point subset of the set contains a point equidistant from the other two. This paper gives a $4$-isosceles set consisting of $7$ points with no three on a line and no four on a circle.