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(2): Fewer than I thought by Jer)

Indeed of the 6 configurations of circles, there are only 3 uniquely shaped/sized triangles.

Petitioning levik is the only way to get a gif on the site.  I don't think it's ever been done in a comment before, but they do appear in puzzles.  But you could put the gif off-site and link to it.

Posted by Charlie on 2004-05-28 11:40:05