We will discuss here about common tangents to two circles.
1. No Common Tangent:
If one circle line completely inside another circle without cutting or touching it at any point then the circles will have no common tangent.
2. One Common Tangent:
If two circles touch each other internally at one point, they will have one common tangent.
3. Two Common Tangents:
If two circles intersect each other at two points, they will have two common tangents.
4. Three Common Tangents:
If two circles touch each other externally at one point, they will have three common tangents.
5. Four Common Tangents:
If two circles do not touch or intersect each other and one does not lie inside the other, they will have four common tangents.
AB and CD are called direct common tangents, and MN and XY are called transverse common tangents.