# MATLAB R2021a

Three points on a circle are given in an input file:

x y

11.5 5

3.2 8.6

-4.5 -6.8

The equation of a circle with radius R and center at (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 = x02 + y02 – R2

Given the coordinates of three points (x1, y1), (x2, y2) and (x3, y3) it is possible to determine the radius and the coordinates of the center of the circle 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, y0 and c.

Write a script which can read an input file in the format shown above. Prompt for the input filename. Calculate the center and radius. Then the write the original coordinates of the three points, the center and radius into an output file having this format:

x y

11.5000 5.0000

3.2000 8.6000

-4.5000 -6.8000

3.8213 -1.3356 center

The original points are shown in columns in the output file which are 15 characters wide with no space in between them. Be sure to prompt for the output filename.

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