![http://en.wikipedia.org/wiki/File:Ptolemy_Equilateral.svg](http://www.futilitycloset.com/wp-content/uploads/2015/03/2015-03-14-a-tidy-theorem1.png)
If an equilateral triangle is inscribed in a circle, then the distance from any point on the circle to the triangle’s farthest vertex is equal to the sum of its distances to the two nearer vertices (above, q = p + r).
(A corollary of Ptolemy’s theorem.)