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?

(In reply to re: Fewer than I thought by GOM)

I'm in the process of drawing all of the solutions with Geometer's Sketchpad.

I've done 5 but I think two of them are making congruent triangles.

I'm not done yet.  Is there a way to post a gif file when I finish?

-Jer

Posted by Jer on 2004-05-28 10:21:32