find furthest point in relative to 2 others

Hi! Here is diagram of my problem:

I need to find point, which is 14m away from point A, and as far as possible, from point B.

Brutforce way, I can simply check radius of circle of point A for every angle:

double x = 14f * Math.Cos(Mathf.Deg2Rad * angle);
double y = 14f * Math.Sin(Mathf.Deg2Rad * angle);

and then compare (x,y) distance to point B.

But is it very long and stupid solution, like I’ll need to run it 360 times for every angle.

What is the most elegant way, using vector math?

Attach this to your target point:

#pragma strict

var A : Transform;
var B : Transform;

function Update () {
	transform.position = A.position + (A.position - B.position).normalized * 14;
}