Three Points Circle Three Points Circle
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Nicola discovered a caliper inside a set of drafting tools he received as a gift. Seeing the caliper, he has decided to learn how to use it.

Through any three points that do not exist on the same line, there lies a unique circle. The points of this circle are represented in a string with the coordinates like so:


Where x1,y1,x2,y2,x3,y3 are digits.

You should find the circle for three given points, such that the circle lies through these point and return the result as a string with the equation of the circle. In a Cartesian coordinate system (with an X and Y axis), the circle with central coordinates of (x0,y0) and radius of r can be described with the following equation:


where x0,y0,r are decimal numbers rounded to two decimal points. Remove extraneous zeros and all decimal points, they are not necessary. For rounding, use the standard mathematical rules.

three_points_circle three_points_circle

Input: Coordinates as a string..

Output: The equation of the circle as a string.


checkio("(2,2),(6,2),(2,6)") == "(x-4)^2+(y-4)^2=2.83^2"
checkio("(3,7),(6,9),(9,7)") == "(x-6)^2+(y-5.75)^2=3.25^2"

How it is used: This equation, also known as Equation of the Circle, comes from the Pythagorean theorem when applied to any point on a circle: the radius is the hypotenuse of a right-angled triangle whose other sides are of length x − a and y − b. Of course you can use this concept for you mathematics software, but we just want to remind about how awesome circles are.

Precondition: All three given points do not lie on one line.
0 < xi, yi, r < 10