What is the formula for calculating the distance between two points of an equilateral triangle with a known "radius"? I have an equilateral triangle with each point being a known distance of N units from the center of the triangle.
What formula would I need to use to determine the length of any side of the triangle?

First draw the lines from all three points to the center point of this triangle, then notice that two if these lines make an isosceles triangle with angles $2\pi/3$, $\pi/6$, and $\pi/6$. Since we're given the length of two of the sides of this triangle, and the angles are known, we can calculate the length of the third side 
Let $a$ denote the length of the inradius, and $b$ the sidelength if the triangle. Then, by the cosine law, we have
$b^2 = a^2 + a^2 - 2aa\cos(2\pi/3)$
$= 2a^2(1 - \cos(2\pi/3)$
$= 2a^2(3/2) $
So we have $b = \sqrt(3a^2)$ or $\sqrt3a$
