Discussion:  All Topics 
Topic:  Common Tangent Construction 
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Subject:  Common Tangent Construction 
Author:  Alan Cooper 
Date:  May 8 2006 
(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 http://www.langara.bc.ca/~acooper/mathlets/CommonTan
(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.)
Alan
 
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