🚀 go-pugleaf

Hi, i'm wondering about the following:

  Given the length of two parallel chords in a circle, and a distance
between them, is there a way to find the length of a middle
parallel chord, that is halfway between the first and second parallel
chord?

  The tough part is that none of these chords are a diameter, so
you don't have a radius to work with.


  To put it another way, let a = 1st chord, b = middle chord, and
c = end chord.		so a > b > c

let's call the difference between a & c, x.
so x/2 would be the difference between a & b, and b & c.

you are given a, c, and x.  Is it possible to find b?

rough diagram:

	----------a-----------  
		  |
		  |
		 x/2
		  |
		  |   
	  --------b--------
		  |
		  |
		 x/2
		  |
		  |
            ------c------

remeber, b is contained inside the circle, as with a and c.
You can use any reasonable value for a, c, and x.

Thanks,
Scott