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

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?

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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
QuestionNo SubjectKevin Tran2004-05-31 19:20:18
Sorry - I'm backAxorion2004-05-30 04:02:30
re: Crossing my fingersCharlie2004-05-28 15:05:04
Crossing my fingersJer2004-05-28 14:36:14
re(3): Fewer than I thoughtCharlie2004-05-28 11:40:05
re(2): Fewer than I thoughtJer2004-05-28 10:21:32
Hints/Tipsre: Fewer than I thoughtDanny2004-05-28 10:09:38
SolutionFewer than I thoughtJer2004-05-28 09:44:39
re(3): are you from Russia?SilverKnight2004-05-27 22:22:04
re(2): are you from Russia?Cory Taylor2004-05-27 21:02:15
:-)Danny2004-05-27 18:13:05
No idea what those o:p's areCharlie2004-05-27 18:08:07
Solutionre: are you from Russia?Charlie2004-05-27 18:05:50
many similar trianglesDanny2004-05-27 18:05:24
Hints/Tipsare you from Russia?Danny2004-05-27 17:49:35
re: the valuesCharlie2004-05-27 17:44:15
Hints/Tipsre(2): solutionDanny2004-05-27 17:37:57
Hints/Tipsre: solutionDanny2004-05-27 17:34:39
I'm not from Russia...Danny2004-05-27 16:50:29
Solutionthe valuesCharlie2004-05-27 16:01:05
Solutionre: solutionCharlie2004-05-27 15:43:44
SolutionsolutionCharlie2004-05-27 15:26:52
re: my old friend PythagorasCharlie2004-05-27 14:42:47
Solutionmy old friend PythagorasDanny2004-05-27 13:52:27
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