Show that there doesn't exist two infinite and separate sets $A,B$ of points such that (i) There are no three collinear points in $A \cup B$, (ii) The distance between every two points in $A \cup B$ is at least $1$, and (iii) There exists at least one point belonging to set $B$ in interior of each triangle which all of its vertices are chosen from the set $A$, and there exists at least one point belonging to set $A$ in interior of each triangle which all of its vertices are chosen from the set $B$.