/** A 2d point with double coords */

class Point2d {
  double x;
  double y;
  
  Point2d(double x, double y) {
    this.x = x;
    this.y = y;
  }

  public Point2d scale(double k) {
    return new Point2d(k*x, k*y);
  }

  public Point2d add(Point2d a) {
    return new Point2d(x+a.x, y+a.y);
  }

  public Point2d subtract(Point2d a) {
    return new Point2d(x-a.x, y-a.y);
  }

  public double length() {
    return Math.sqrt(x*x+y*y);
  }
  
  public Point2d normalize() {
    return scale(1/length());
  }
  
  public double length2() {
    return x*x+y*y;
  }
  
  public double angle() {
    return Math.atan2(y,x);
  }

  public static Point2d fromPolar(double r, double theta) {
    return new Point2d(r*Math.cos(theta), r*Math.sin(theta));
  }

 public Point2d circleCentre(Point2d a, Point2d b) {
   double d1 = length2();
   double d2 = a.length2();
   double d3 = b.length2();
   double divisor = 2*(y*(b.x-a.x) + a.y*(x-b.x) + b.y*(a.x-x));
   return new Point2d((y*(d3-d2) + a.y*(d1-d3) + b.y*(d2-d1))/divisor,
		      -(x*(d3-d2) + a.x*(d1-d3) + b.x*(d2-d1))/divisor);
 }

  public String toString() {
    return "("+Double.toString(x)+","+Double.toString(y)+")";
  }
}