Hello, strewart!

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. Code:

C
*
b * * a
* * *
* *
A * - - - - * - - - - * B
* *
r * β * α * r
* *
*
O

We have on a circle with center and radius

. .

Let

In , Law of Cosines:

. .

. .

Hence, we have: .

. .

Substitute [4] and [5]:

. .

. . . . . .

And now, *all we have to do* is: eliminate the radicals and solve for *r.*