Separation

Two distinct point pairs $AC$ and $BD$ separate each other if $A$, $B$, $C$, and $D$ lie on a Circle (or line) in such order that either of the arcs (or the line segment $AC$) contains one but not both of $B$ and $D$. In addition, the point pairs separate each other if every Circle through $A$ and $C$ intersects (or coincides with) every Circle through $B$ and $D$. If the point pairs separate each other, then the symbol $AC//BD$ is used.