Given:

Three circles A, B and C.

Each circle is tangent to the other two.

The radius of A is 20.

The radius of B is 30.

Questions:

How many unique values of radius C exist where the centers of A, B and C form a right triangle? (Unique: Do not count triangles which are equal through flips and rotations. You may only count dissimilar triangles and similar triagles of differing sizes.)

What are the values?

I'm no longer much of a programmer.  I've never made a web page with an image in it but I think I got it right.

http://www.mohawk.k14.mass.edu/Highschool/DEPT/math/galvagni/square_circle.htm

The 6 cases are shown in 3 pictures.   Two are at the same scale so the triangles can be seen to be the same size.  The third is expanded so that details can be seen. 

If you want the Geometer's Sketchpad file, just email me.

-Jer

Posted by Jer on 2004-05-28 14:36:14