Will B. Lofty <firstname.lastname@example.org> 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 email@example.com http://www.ics.uci.edu/~eppstein/