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 Square Circles (Posted on 2004-05-27)
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.)
 re(3): Fewer than I thought | Comment 20 of 24 |
(In reply to re(2): Fewer than I thought by Jer)

Indeed of the 6 configurations of circles, there are only 3 uniquely shaped/sized triangles.

Petitioning levik is the only way to get a gif on the site.  I don't think it's ever been done in a comment before, but they do appear in puzzles.  But you could put the gif off-site and link to it.

 Posted by Charlie on 2004-05-28 11:40:05

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