Construct the common tangents to given circles


 

 

Given two circles AB and CD, find the common tangent lines.

The key to this problem is to find the point J where the tangent lines intersect. But this point J can be viewed as the center of a dilation that takes one circle to the other, so J is collinear with any points in the two circles corresponding by the dilation. Thus take any line through A and intersect with circle AB and intersect a parallel line through c with circle CD. Intersect the line of centers with a line connecting a pair of intersection points to find J.

 

 

 

 

Click here for GSP file.

Click here for the GSP script


Once J is constructed, just construct the tangents to either of the circles through J, and they will automatically be tangent to the other circle.

 

By connecting a different pair of the intersection points, you can find another point that is center of dilation and is the intersection point of the common internal tangents, if they exist. If one circle is interior to the other, the two centers of dilation exist, but there are no common tangents.


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