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Topic: Three concentric circles and a triangle
Replies: 5   Last Post: Jun 2, 2000 6:41 PM

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 eppstein@euclid.ics.uci.edu Posts: 128 Registered: 12/8/04
Re: Three concentric circles and a triangle
Posted: Jun 1, 2000 1:34 PM

Will B. Lofty <will_bl@my-deja.com> writes:
> Given three concentric circles of radii r1, r2, r3 (r1 < r2 < r3), is it
> possible to find an equilateral triangle ABC so that A is on the inner
> circle, B is on the middle circle, and C is on the outer circle?

You at least need an additional condition on the radii.
If 2r1 < r3 - r2, then |AB| <= r1+r2 < r3-r2 <= |AC|
and the triangle can not be equilateral.

I don't think 2r1 < r3 - r2 is the tight inequality, either, because it
is not possible for |AB|=r1+r2 and |AC|=r3-r2 unless B and C are
opposite, which can't happen for an equilateral triangle.
--
David Eppstein UC Irvine Dept. of Information & Computer Science
eppstein@ics.uci.edu http://www.ics.uci.edu/~eppstein/

Date Subject Author
6/1/00 will_bl@my-deja.com
6/1/00 eppstein@euclid.ics.uci.edu
6/1/00 macavity
6/1/00 dannyboy@here.com
6/2/00 spamless@nil.nil
6/2/00 Barry Sanders