// Locate the intersection(s) of 2 circles 
// thanks to jupdike/IntersectTwoCircles.js
// https://gist.github.com/jupdike/bfe5eb23d1c395d8a0a1a4ddd94882ac

// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);

const radius = 40; // min=5  max=100 step=1
const X1 = -14; // min=-100  max=100 step=1
const Y1 = -12; // min=-100  max=100 step=1
const X2 = 28; // min=-100  max=100 step=1
const Y2 = 23; // min=-100  max=100 step=1

// Global code will be evaluated once.
const turtle = new Turtle();

centeredCircle(X1, Y1, radius, 360);
centeredCircle(X2, Y2, radius, 360);

intersectTwoCircles(X1, Y1,radius, X2, Y2 ,radius)

// thanks to jupdike/IntersectTwoCircles.js
// https://gist.github.com/jupdike/bfe5eb23d1c395d8a0a1a4ddd94882ac
// 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;

  centeredCircle(ix1, iy1, 2, 360);  // highlight intersection point 1
  centeredCircle(ix2, iy2, 2, 360);  // highlight intersection point 1

  // 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];
}


// thanks to Reinder for this function
// Draws a circle centered a specific x,y location 
// and returns the turtle to the original angle after it completes the circle.
function centeredCircle(x,y, radius, ext) {
turtle.penup();
turtle.goto(x,y);
turtle.backward(radius);
turtle.left(90);
turtle.pendown(); turtle.circle(radius, ext);
turtle.right(90); turtle.penup(); turtle.forward(radius); turtle.pendown();
}