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Square Circles (Posted on 2004-05-27) Difficulty: 3 of 5
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?

See The Solution Submitted by Axorion    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
I'm not from Russia... | Comment 6 of 25 |
(In reply to re: my old friend Pythagoras by Charlie)

"...There's more to it than that...The specific numbers you mention might not be possible given this condition..."

...but I was rushing. You're right there are many combinations that I didn't initially think of, but still why wouldn't the numbers I gave work? If all 3 circles are external to each other then I think the numbers add up.


  Posted by Danny on 2004-05-27 16:50:29
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