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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)

 Subject Author Date No Subject Kevin Tran 2004-05-31 19:20:18 Sorry - I'm back Axorion 2004-05-30 04:02:30 re: Crossing my fingers Charlie 2004-05-28 15:05:04 Crossing my fingers Jer 2004-05-28 14:36:14 re(3): Fewer than I thought Charlie 2004-05-28 11:40:05 re(2): Fewer than I thought Jer 2004-05-28 10:21:32 re: Fewer than I thought Danny 2004-05-28 10:09:38 Fewer than I thought Jer 2004-05-28 09:44:39 re(3): are you from Russia? SilverKnight 2004-05-27 22:22:04 re(2): are you from Russia? Cory Taylor 2004-05-27 21:02:15 :-) Danny 2004-05-27 18:13:05 No idea what those o:p's are Charlie 2004-05-27 18:08:07 re: are you from Russia? Charlie 2004-05-27 18:05:50 many similar triangles Danny 2004-05-27 18:05:24 are you from Russia? Danny 2004-05-27 17:49:35 re: the values Charlie 2004-05-27 17:44:15 re(2): solution Danny 2004-05-27 17:37:57 re: solution Danny 2004-05-27 17:34:39 I'm not from Russia... Danny 2004-05-27 16:50:29 the values Charlie 2004-05-27 16:01:05 re: solution Charlie 2004-05-27 15:43:44 solution Charlie 2004-05-27 15:26:52 re: my old friend Pythagoras Charlie 2004-05-27 14:42:47 my old friend Pythagoras Danny 2004-05-27 13:52:27

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