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 the values by Charlie)

... the last case:

If A and B are externally tangent to each other but internal to C but this time the right angle is at the center of B, (r-30)^2 + 50^2 = (r-20)^2; r = 150.

Posted by Charlie on 2004-05-27 17:44:15