Question 45
Find out whether or not there exist two disjoint infinite sets $A$ and $B$ in the plane satisfying the following conditions:
(i) No three points in $A \cup B$ are collinear and the distance of any pair of points in $A \cup B$ is at least $1$.
(ii) There is a point of $A$ in any triangle whose vertices are in $B$ and there is a point of $B$ in every triangle whose vertices are in $A$.
(i) No three points in $A \cup B$ are collinear and the distance of any pair of points in $A \cup B$ is at least $1$.
(ii) There is a point of $A$ in any triangle whose vertices are in $B$ and there is a point of $B$ in every triangle whose vertices are in $A$.