Chapter 4, Problem 21P

The equation of a circle in a plane with radius R and a center at point (x₀, y₀) is given by:

(x-x₀)2+(y-y₀)2=R² The equation can also be written in the form:

-2x₀x-2y₀y+c=- (x²+y²) where c =x²₀+ y²₀-R² Given the coordinates of three points (x₁, y₁) (x₂, y_2), and (x₃, y₃) it is possible to determine the radius and the coordinates of the center of the circ le that passes through the three points. This is done by substituting the coordinate of each of the points in the equation and solving the system of three linear equations for x₀, y_0, and c.

Write a program in a script file that calculates the coordinates of the center and the radius of a circle that passes through three given points. When executed the program asks the user to enter the coordinates of the three points. The program then calculates the center and radius and displays the results in the following format: “The coordinates of the center are (xx.x, xx.x) and the radius is xx.x.”, where xx.x stands for the calculated quantities rounded to the nearest tenth. Execute the program entering the following three points: (11.5, 5). (3.2, 8.6). and (-4.5, -6.8).