One circle is completly outside the other. |AB| gt; r_1 + r_2. Circles touch externally. |AB| = r_1 + r_2. Circles intersect at two points. |r_1 - r_2| < |AB| < r_1 + r_2. Circles touch internally |AB| = |r_1 - r_2|. One circle is completly inside the other |AB| < |r_1 - r_2|. Circles have common center.