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.
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?