Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Three concentric circles and a triangle
Replies:
5
Last Post:
Jun 2, 2000 6:41 PM




Re: Three concentric circles and a triangle
Posted:
Jun 1, 2000 1:34 PM


Will B. Lofty <will_bl@mydeja.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 < r3r2 <= 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=r3r2 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/



