Common tangents are lines that touch two or more circles at the same time without intersecting the circles. They can be categorized into Direct Common Tangents and Transverse Common Tangents, depending on whether they lie outside or inside the circles respectively.

Number of Common Tangents

The number of common tangents depends on the position and size of the two circles.

Case 1: There are 4 common tangents if the circles are neither touching nor intersecting

 

Case 2: There are 3 common tangents if the circles are touching externally

 

Case 3: There are only two common tangents if circles are intersecting each other.

 

Case 4: There is only one tangent if the circles are internally touching each other

Case 5: There is no common tangent if one circle is contained in the second circle.