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Topic: tangent circles
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Steve Weimar

Posts: 24
Registered: 12/3/04
tangent circles
Posted: Nov 26, 1993 3:32 PM
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[As indicated, I found this on rec.puzzles and thought it might be of
interest here as well. Please note that I am not the author. -- steve]

Newsgroups: rec.puzzles
From: rolls@cis.umassd.edu (Frank Pinto)
Subject: Circles, circles, circles......puzzle.
Organization: University of Massachusetts Dartmouth
Date: Mon, 22 Nov 1993 18:28:21 GMT

Hello all
Here is an interesting one:

Have a good time

Frank Pinto

--------------begin------------



Start with a circle O of radius 1 and let a and b be arbitrary real
numbers.
Construct a first circle of radius a tangent to circle O.
Construct a 2nd circle of radius b tangent to O and the a-circle.
Construct a 3rd circle of radius b/a tangent to O and the b-circle.
Construct a fourth circle of radius 1/a tangent to O and the b/a-circle.
Construct a fifth circle of radius 1/b tangent to O and the 1/a-circle.
Construct a sixth circle of radius a/b tangent to O and the 1/b-circle.

Note that each new radius is the ratio of the two preceding radii.

Prove that the sixth circle is tangent to the first circle.

--suggested by Bruce Hanson, St. Olaf College
--
Frank Pinto (XICO)| The roots of education are bitter,
Mathematics, | but the fruit is sweet.
Computer Science &|
Philosophy | ARISTOTLE





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