I have an approach, but I did not finish the problem . . .
As part of an experiment I am doing, I need a radius for a circle.
I have the lengths of three segments connecting the three points on the circle.
Is there a way to work out the radius of the circle from that?
I know with two points, the circle could be any size, .Right!
but with 3 points there should only be one solution for a circle through all three. .Yes!
I've tried various simultaneous equations and not been able to come up with a solution.
I always end up with 2 unknowns in any equation I make.
Any help would be appreciated.
b * * a
* * *
A * - - - - * - - - - * B
r * β * α * r
We have on a circle with center and radius
In , Law of Cosines:
Hence, we have: .
Substitute  and :
. . . . . .
And now, all we have to do is: eliminate the radicals and solve for r.