Two circles on a Cartesian plane, A and $B,$ are each defined by three descriptors:

$x$ the $x-$coordinate of the circle's center

$,$ the $y-$coordinate of the circle's center

R$.$ the radius of the circle

Circles A and $B$ will both be centered either on the and $Y_B=0,,$ or on the $Y-$axis $($i$.$e$.x_A=0$ and $x_B=0,$ but not both.

A pair of circles $($ A and $B)$ will have one of the following relationship types:

Touching they touch each other at a single point

Concentric they have the same center point

Intersecting they intersect each other $($touching at two points$)$

Disjoint$-$Outside: disjoint with one existing outside of the other

Disjoint$-$Inside: disjoint with one contained inside the other $($but not concentric$)$