Circle Through Three Points

Time limit1sMemory limit128 MB

Summary

For each line of three points, compute the circle through them and print its center-radius and general equations with signs adjusted.

Level: Easy3 of 10
Topics: Geometry, Math, Implementation, Brute force
Solved: No attempts yet

Problem

Given the Cartesian coordinates of three points on a plane, find the equation of the circle that passes through all three of them. The three points are guaranteed not to lie on a single straight line.

Report the circle in two forms. One is the standard (center–radius) form

$(x - h)^2 + (y - k)^2 = r^2$

and the other is the general form

$x^2 + y^2 + cx + dy - e = 0$

Input

Each line of input contains the $x$ and $y$ coordinates of three points $A$ , $B$ , and $C$ , listed in the order $A_x$ , $A_y$ , $B_x$ , $B_y$ , $C_x$ , $C_y$ . The coordinates are real numbers separated from one another by one or more spaces. Read lines until the end of the input.

Output

For each input line, print the two required equations on two consecutive lines, using the format shown in the examples. The values $h$ , $k$ , $r$ , $c$ , $d$ , and $e$ must each be printed with exactly three digits after the decimal point.

Adjust the plus and minus signs so that no number is preceded by two signs. For example, when $k = -2$ the term is written (y + 2.000) rather than (y - -2.000). Every +, -, and = sign must be surrounded by exactly one space on each side, and no other spaces may appear inside an equation.

Separate consecutive equation pairs with a single blank line.

Hint

Examples3

Example 1

Input

7.0 -5.0 -1.0 1.0 0.0 -6.0
1.0 7.0 8.0 6.0 7.0 -2.0

Expected output

(x - 3.000)^2 + (y + 2.000)^2 = 5.000^2
x^2 + y^2 - 6.000x + 4.000y - 12.000 = 0

(x - 3.921)^2 + (y - 2.447)^2 = 5.409^2
x^2 + y^2 - 7.842x - 4.895y - 7.895 = 0

Example 2

Input

18 5 5 18 0 -7

Expected output

(x - 5.000)^2 + (y - 5.000)^2 = 13.000^2
x^2 + y^2 - 10.000x - 10.000y - 119.000 = 0

Example 3

Input

4 2 -6 12 -14 -4

Expected output

(x + 6.000)^2 + (y - 2.000)^2 = 10.000^2
x^2 + y^2 + 12.000x - 4.000y - 60.000 = 0