Simple trilateration algorithm implementation in JavaScript.

trilateration.js

function getTrilateration(position1, position2, position3) {
    var xa = position1.x;
    var ya = position1.y;
    var xb = position2.x;
    var yb = position2.y;
    var xc = position3.x;
    var yc = position3.y;
    var ra = position1.distance;
    var rb = position2.distance;
    var rc = position3.distance;

    var S = (Math.pow(xc, 2.) - Math.pow(xb, 2.) + Math.pow(yc, 2.) - Math.pow(yb, 2.) + Math.pow(rb, 2.) - Math.pow(rc, 2.)) / 2.0;
    var T = (Math.pow(xa, 2.) - Math.pow(xb, 2.) + Math.pow(ya, 2.) - Math.pow(yb, 2.) + Math.pow(rb, 2.) - Math.pow(ra, 2.)) / 2.0;
    var y = ((T * (xb - xc)) - (S * (xb - xa))) / (((ya - yb) * (xb - xc)) - ((yc - yb) * (xb - xa)));
    var x = ((y * (ya - yb)) - T) / (xb - xa);

    return {
        x: x,
        y: y
    };
}

The issue is that the code assumes that the 'a' and 'b' points don't have the same 'x' co-ordinate. It's the var x = line ending in '/ (xb - xa)'. They need to be different to avoid a divide by zero. Swap your 2nd and 3rd points and it'll work.

Here is a link back to the author's youtube video with the use case: https://www.youtube.com/watch?v=dMWEl6GBGqk

Just posted another trilateration, based on the Wikipedia derivation. I believe it is easier to follow it, also it is working in 3D space and returns [ 39.996, 99.996, +/-0.53 ] for your example input, @ravisharma1987 (can be configured to return the middle, then it returns [ 39.996, 99.996, 0 ]).
https://github.com/gheja/trilateration.js

Hey guys!

I did an example using p5js.org

Thanks @kdzwinel for the help with the math!