When two circles touch each other, it is possible to draw a circle with two centres and the point of contact of two circles.

When two circles do not touch or do not intersect, the maximum number of common tangents that can be drawn to two circles is two.

Two circles do not intersect each other in more than two points.

The maximum number of common tangents of two circles which intersect each other externally is two.

The maximum number of tangents that can be drawn to a circle from a point outside the circle is one.