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Topic: Common Tangent Construction

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Subject:   Common Tangent Construction
Author: Alan Cooper
Date: May 8 2006
On Apr 10 2006, Mathman wrote:
(in another thread in the 'All Tools on a Calculator' Discussion)
> ...I taught mathematics, and found a lifetime of "rich imagery" in
> Euclid as well as all other studies.  Here's a simple example, and I
> wonder how it might be done differently or better without compasses
> and straightedge:

> The problem is to draw tangents to two circles.
> If the same size, there is no problem, the construction being
> basically a rectangle.  If one circle is noteably smaller than the
> other, there is a technique that is not too demanding, simple in
> fact.  If the circles are close in radii, but not equal, then the
> first is not possible, and the second is not feasible because of
> limit of distance required using the same technique, and the problem
> becomes a pretty problem [which I had solved and was able to
> demonstrate or offer to keen students.]

I thought it would be interesting to give a dynamic illustration of the
construction that (I presume) you had in mind.

The result is at

(This is not intended to replace the use of concrete drawing tools, but rather
just to make it possible for the student to see how the construction works in a
greater range of cases than it woud be possible to deal with by hand.)


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