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.
You are watching: How many tangents that are common to both circles can be drawn?
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?
I’ve summarised the class in the adhering to table:
|Position||Number of common Tangents|
|Lying exterior each other||4|
|Intersecting at 2 points||2|
|One lying within other||0|
In the next lesson, i’ll talk about the equations of these typical tangents.