Find the intersections (two points) of two circles, if they intersect at all

IntersectTwoCircles.js

// based on the math here:
// http://math.stackexchange.com/a/1367732

// x1,y1 is the center of the first circle, with radius r1
// x2,y2 is the center of the second ricle, with radius r2
function intersectTwoCircles(x1,y1,r1, x2,y2,r2) {
  var centerdx = x1 - x2;
  var centerdy = y1 - y2;
  var R = Math.sqrt(centerdx * centerdx + centerdy * centerdy);
  if (!(Math.abs(r1 - r2) <= R && R <= r1 + r2)) { // no intersection
    return []; // empty list of results
  }
  // intersection(s) should exist

  var R2 = R*R;
  var R4 = R2*R2;
  var a = (r1*r1 - r2*r2) / (2 * R2);
  var r2r2 = (r1*r1 - r2*r2);
  var c = Math.sqrt(2 * (r1*r1 + r2*r2) / R2 - (r2r2 * r2r2) / R4 - 1);

  var fx = (x1+x2) / 2 + a * (x2 - x1);
  var gx = c * (y2 - y1) / 2;
  var ix1 = fx + gx;
  var ix2 = fx - gx;

  var fy = (y1+y2) / 2 + a * (y2 - y1);
  var gy = c * (x1 - x2) / 2;
  var iy1 = fy + gy;
  var iy2 = fy - gy;

  // note if gy == 0 and gx == 0 then the circles are tangent and there is only one solution
  // but that one solution will just be duplicated as the code is currently written
  return [[ix1, iy1], [ix2, iy2]];
}

A simple TypeScript adaptation:

interface Point {
  x: number;
  y: number;
}

interface Circle {
  cx: number;
  cy: number;
  r: number;
}

const intersectCircleCircle = (c1: Circle, c2: Circle): Point[] => {
  const { cx: x1, cy: y1, r: r1 } = c1;
  const { cx: x2, cy: y2, r: r2 } = c2;

  const centerdx = x1 - x2;
  const centerdy = y1 - y2;
  const R = Math.sqrt(centerdx * centerdx + centerdy * centerdy);
  if (!(Math.abs(r1 - r2) <= R && R <= r1 + r2)) {
    // no intersection
    return []; // empty list of results
  }
  // intersection(s) should exist

  const R2 = R * R;
  const R4 = R2 * R2;
  const a = (r1 * r1 - r2 * r2) / (2 * R2);
  const r2r2 = r1 * r1 - r2 * r2;
  const c = Math.sqrt((2 * (r1 * r1 + r2 * r2)) / R2 - (r2r2 * r2r2) / R4 - 1);

  const fx = (x1 + x2) / 2 + a * (x2 - x1);
  const gx = (c * (y2 - y1)) / 2;
  const ix1 = fx + gx;
  const ix2 = fx - gx;

  const fy = (y1 + y2) / 2 + a * (y2 - y1);
  const gy = (c * (x1 - x2)) / 2;
  const iy1 = fy + gy;
  const iy2 = fy - gy;

  // note if gy == 0 and gx == 0 then the circles are tangent and there is only one solution
  // but that one solution will just be duplicated as the code is currently written
  return [
    { x: ix1, y: iy1 },
    { x: ix2, y: iy2 },
  ];
};