If the distance between the centres of two circles is less than the sum of radii of the two, then they:

Let $d$ be the distance between centres, and $r_1,r_2$ be the radii of the two circles.If $d=r_1+r_2$, they touch externally.If $d=|r_1-r_2|$, they touch internally.If $|r_1-r_2|<d<r_1+r_2$, they intersect each other at two points.Therefore, if the distance is less than the sum of radii, the circles intersect each other.