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tangent circles
Posted:
Nov 26, 1993 3:32 PM


[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 acircle. Construct a 3rd circle of radius b/a tangent to O and the bcircle. Construct a fourth circle of radius 1/a tangent to O and the b/acircle. Construct a fifth circle of radius 1/b tangent to O and the 1/acircle. Construct a sixth circle of radius a/b tangent to O and the 1/bcircle.
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



