Get the equation, center, and radius of a circle given 3 points on its circumference.

circumscribe.js

/** 
 * circumscribe(Number x1, Number y1, Number x2, Number y2, Number x3, Number y3)
 * 
 * Returns an object describing the circle's center, radius, and equation in Standard Form.
 * Returns an error if points are overlapping or on the same line.
 * Example: `circumscribe(5, -3, -1, -3, 2, -6)` returns {circumcenter: [2, -3], equation: "(x-2)²+(y+3)²=9", radius: 3}
 **/
 
function circumscribe(x1, y1, x2, y2, x3, y3)  {
    // It took some math to figure this out but I'll never tell you how 😈
    let s1 = (x1-x2)/(y2-y1), s2 = (x2-x3)/(y3-y2),
        pts = [[x1, y1], [x2, y2], [x3, y3]];
    if (arguments.length < 6 || [...arguments].some(n => typeof n !== "number")) {
      return Error("CircumscribeError: Must provide exactly 3 numeric (x,y) points");
    }
    if (s1 === s2 || pts.some((pt, idx) => pts.some((_pt, _idx) => _idx !== idx && pt.every((v, __idx) => v === _pt[__idx]))) || [s1, s2].every(s => [Infinity, -Infinity].includes(s))) {
        return Error("CircumscribeError: Points must be independent and not collinear");
    }
    let m1 = [(x1+x2)/2, (y1+y2)/2], m2 = [(x2+x3)/2, (y2+y3)/2];
    let x = (m2[1]-m1[1]+s1*m1[0]-s2*m2[0])/(s1-s2);
    let y = s1*x+m1[1]-s1*m1[0];
    if (Math.abs(s1) === Infinity) [x, y] = [m1[0], s2*m1[0]+m2[1]-s2*m2[0]];
    if (Math.abs(s2) === Infinity) [x, y] = [m2[0], s1*m2[0]+m1[1]-s1*m1[0]];
    let radiusSquared = Math.round((Math.pow(x-x1, 2) + Math.pow(y-y1, 2))*1000)/1000;
    [x, y] = [x, y].map(n => Math.round(n*1000)/1000);
    let equation = `${x === 0 ? "x" : `(x${x < 0 ? "+" : ""}${-x})`}²+${y === 0 ? "y" : `(y${y < 0 ? "+" : ""}${-y})`}²=${radiusSquared}`;
    return {
        circumcenter: [x, y],
        radius: Math.sqrt(radiusSquared),
        equation,
    };
}