perplexus.info :: Geometry : Square Circles

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: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-07-08 23:41:46
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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