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)

"If A and B are externally tangent to each other but internal to C, then if the right angle is at the center of C then, (r-30)^2 +(r-20)^2 = 50^2; so r = 60"

That's another 30 40 50 triangle. I thought that only dissimilar triangles were allowed. If I'm missunderstaning please forgive me. I know you found that triangle by a completely different means than the one were all 3 circles were external to each other but the triangle is still the same. In that case the answer would be there's only 3 possible right triangles to find.

• 30 40 50
• 10 24 26
• 50 120 130

Posted by Danny on 2004-05-27 18:05:24