Illustrated · 1 min
The common external tangent of two circles is the line that is tangent to both circles. The points of tangency are distinct and does not pass in between the circles like a common internal tangent.
The pink line is a common external tangent
number of circles can have a common external tangent as long as they all share a line of tangency (and as long as ).
Three circles sharing a common tangent
When there are two circles, there will almost always be two common external tangents, as shown below:
Having two external tangents, however, is certainly not limited to just two circles!
Three circles with two common external tangents (overlapping circles are fine, though concentric (sharing center) wouldn't work.)
Two or more circles that are internally tangent and share a point of tangency will have only one common external tangent:
Common external tangent line of internally tangent circles