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| Ring of Circles (Posted on 2013-08-17) |
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Define a Ring of Circles ROC(n,r,P,a) as a set of
n≥3 circles (each with radius r, each with center on
a circle with center P and radius a, and each
externally tangent to both its neighbors).
With b>a, each of the circles in ROC(6,R,P,b)
is externally tangent to two of the circles in
ROC(6,r,P,a).
What is the ratio b/a?
Extra credit - what is the ratio if 6
is replaced with n in the problem?
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Submitted by Bractals
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Rating: 4.0000 (1 votes)
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Solution:
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(Hide)
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See Harry's post for the solution.
Note that the smallest root of the quadratic
satisfies b<a and that the product of the
roots is one.
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Subject |
Author |
Date |
 | Solution | Harry | 2013-08-21 10:46:48 |
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