1. 
package acm_190_circle_through_three_points;

import java.util.Scanner;

/**
 * FWP, AusgewŠhlte Probleme aus dem ACM Programming Contest, SS10 
 * Problem: acm_190_circle_through_three_points
 * Link: 
 * 
 * @author Martin Lambeck
 * @version 1.0, 07.09.2010
 * 
 * Method : geometry
 * Status : Accepted
 * Runtime: 0.168
 */


public class Main
{
	static Point p1;
	static Point p2;
	static Point p3;

	static Scanner sc = new Scanner(System.in);

	public static void main (String...args)
	{
		while (testcase());
	}

	public static boolean testcase()
	{
		double x, y;
		double frac, denom;
		double r;


		if (!sc.hasNextDouble())
			return false;

		p1 = new Point(sc.nextDouble(), sc.nextDouble());
		p2 = new Point(sc.nextDouble(), sc.nextDouble());
		p3 = new Point(sc.nextDouble(), sc.nextDouble());

		Point m1 = mid(p1, p2); //middle point of p1->p2
		Point m2 = mid(p2, p3); //middle point of p2->p3

		Vector v1 = ortho(m1, p2); //v1 orthogonal to m1->p2 
		Vector v2 = ortho(m2, p3); //v2 orthogonal to m2->p3


		// m1 + t * v1 = m2 + s * v2
		//
		// I)   m1.x + t * v1.x = m2.x + s * v2.x
		// II)  m1.y + t * v1.y = m2.y + s * v2.y
		//
		// t = ... * s
		// eliminate t => s = ... = frac
		//
		// x,y = center of circle = m2 + v2 * s = m2 + v2 * frac

		denom = (v1.y * v2.x - v1.x * v2.y);
		frac = (v1.x * (m2.y - m1.y) - v1.y * (m2.x - m1.x)) / denom;

		if (denom == 0)
			throw new IllegalArgumentException(); //wont happen, there is no such testcase

		x = m2.x + v2.x * frac;
		y = m2.y + v2.y * frac;


		r = Math.hypot(p1.x - x, p1.y - y);

		String sx = (x < 0 ? "+" : "-");
		String sy = (y < 0 ? "+" : "-");
		
		System.out.printf("(x %s %.3f)^2 + (y %s %.3f)^2 = %.3f^2%n", sx, Math.abs(x), sy, Math.abs(y), r);

		
		double sq = x*x + y*y - r*r;
		
		String ssq = (sq < 0 ? "-" : "+");
		
		System.out.printf("x^2 + y^2 %s %.3fx %s %.3fy %s %.3f = 0%n%n", sx, Math.abs(2*x), sy, Math.abs(2*y), ssq, Math.abs(sq));

		
		return true;
	}

	public static Point mid(Point p1, Point p2)
	{
		double x = (p2.x - p1.x) / 2.0 + p1.x;
		double y = (p2.y - p1.y) / 2.0 + p1.y;

		return new Point (x, y);
	}
	public static Vector ortho(Point p0, Point q)
	{
		double x = q.x - p0.x;
		double y = q.y - p0.y;

		return new Vector(y, -x);
	}

}

class Point
{
	double x;
	double y;

	public Point(double xx, double yy)
	{
		x = xx;
		y = yy;
	}
}

class Vector
{
	double x;
	double y;

	public Vector(double xx, double yy)
	{
		x = xx;
		y = yy;
	}
}