How can I work out the length of the sides of an Equilateral triangle that exists in a circle? I'm making a game and need a bit of mathematics help.
If I have a circle with a radius of $x$ and there is an equilateral triangle in the center made up of $3$ equal chords. How can I work out the length of the sides of the triangle?
I actually want to split the equilateral triangle into $3$ different isosceles triangles(making a straight line from the center to the corner of the equilateral triangle). The $2$ equal sides are obviously $\frac x2$ in length. But the last side's length eludes me. 
I'd prefer not to use trig. Computers generally don't like any form of roots. But I can probably find a way to optimize it if that's my only solution. 
Thanks in advance.
Triangle I added this Image for clarity. I need the value y.
 A: No trig is needed for the answer, though the law of Cosines gives a direct approach.
To do it via basic geometry, draw a radius out to one of the vertices.  By Symmetry it bisects the angle there.  Dropping the perpendicular out to a side of the equilateral triangle, gives us a $30-60-90$ right triangle with hypotenuse $x$, the radius of the circle.  Of course, the side opposite the $60$ degree angle has length $\frac {\sqrt 3}2\,x$ from which it follows that the length of one side of the equilateral triangle is $$\boxed {\sqrt 3\,x}$$
A: This is what I used to do before I came to know about trigonometry.

Let $BD$ be the median. 
Medians of an equilateral triangle pass through the circumcenter. So circumcenter is the centroid of triangle. Centroid divide median in $\frac21$. So $\frac{BO}{OD}=\frac21 \implies BD=\frac{3x}{2}$. $BD$ is also the altitude of the triangle. Now altitude of an equilateral triangle of side $a$ is equal to $\frac{a\sqrt3}{2}$. $$\frac{a\sqrt3}{2}=\frac{3x}{2}\\
a=\frac{3x}{\sqrt3}=\sqrt3x$$
