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 solution by Charlie)

Actually count two more: as the circle C increases in either of the cases where A and B are extenally tangent, it also passes a point at which its own center is the right angle.

This brings the total to 6.

Posted by Charlie on 2004-05-27 15:43:44