This lesson will certainly talk about variety of common tangents come two offered circles. This will rely upon the relative position of the two circles – something which i talked about in the ahead lesson. Let’s revisit every the cases.

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Lying outside Each Other

In this case, there will be four typical tangents. Have actually a look.


The tangents intersecting in between the one are recognized as transverse typical tangents, and also the other two are referred to as the direct typical tangents.

Touching Each various other Externally

In this case, there will be three usual tangents, as presented below.


The tangent in in between can be thought of as the transverse tangents coinciding together.

Intersecting Each various other at 2 Points

In this case, there will certainly be two common tangents.


Touching Each other Internally

In this case, there will certainly be just one common tangent, as shown in the figure.


Think the is together the two tangents in the previous situation coinciding into one, as soon as one that the one is moved towards the other.

One Lying within Another

In this case, there will certainly be no common tangent, as any line touching the within circle will always intersect the external circle at 2 points.

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Here’s a simulation that reflects the common tangents to 2 circles.

You have the right to drag the four blue points, and observe the number of common tangents come the two circles. Go this align with what we disputed above?

Lesson Summary

I’ve summarised the class in the adhering to table:

PositionNumber of common Tangents
Lying exterior each other4
Touching externally3
Intersecting at 2 points2
Touching internally1
One lying within other0

In the next lesson, i’ll talk about the equations of these typical tangents.