circle-circle-intersection.js

const { lvar, add, sub, mul, and, between, run } = require("logicjs");

const circle = ({ a, b, r, x, y }) => {
  const xMinusA = lvar();
  const yMinusB = lvar();

  const xMinusASquared = lvar();
  const yMinusBSquared = lvar();

  const rSquared = lvar();

  return [
    sub(x, a, xMinusA), // x−a
    sub(y, b, yMinusB), // y−b

    mul(xMinusA, xMinusA, xMinusASquared), // (x−a)^2
    mul(yMinusB, yMinusB, yMinusBSquared), // (y−b)^2

    mul(r, r, rSquared), // r^2

    add(xMinusASquared, yMinusBSquared, rSquared), // (x−a)^2 + (y−b)^2 = r^2
  ];
};

const x = lvar();
const y = lvar();

const constraints = [
  between(-10, 10, x),
  between(-10, 10, y),

  // https://planetcalc.com/8098/?x1=0&y1=0&r1=5&x2=10&y2=0&r2=5
  ...circle({ a: 0, b: 0, r: 5, x, y }),
  ...circle({ a: 10, b: 0, r: 5, x, y }),
];

const result = run(and(...constraints), [x, y]);
console.log(result); // [ [ 5, 0 ] ]