# Circumscribed Circle of a Triangle

Time Limit : 1 sec, Memory Limit : 131072 KB
Japanese version is here

# Circumscribed Circle of A Triangle.

Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.

## Input

Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$

in a line. All the input are real numbers.

## Output

For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.

## Constraints

• $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$
• $n \leq 20$

## Sample Input

1
0.0 0.0 2.0 0.0 2.0 2.0


## Output for the Sample Input

1.000 1.000 1.414


Source: PC Koshien 2003 , All-Japan High School Programming Contest, Aizu-Wakamatsu, Japan, 2003
http://www.pref.fukushima.jp/pc-concours/