If you don't have any mathematical data to start with, you need to approximate the coordinates of three points along the circle. Some example data will help you understand.
Choose three points that lie on the circle. Mark these points as “A,” “B,” and “C” then record their approximate coordinates in the form (x,y). In our example A = (0,6), B = (5,11), and C = (10,6).
Using a compass, draw a complete circle with the center being point A, and draw another circle of the same radius using point B as a center. If done correctly, circles A and B will intersect at exactly two points which we will label “M” and “N.” Draw a line through points M and N making sure that the line MN passes through the apparent center of the circle.
Using the same radius that you used to draw circles A and B, draw a third circle using point C as the center. Circle C will intersect circle B in exactly two points which we will label “O” and “P.” Draw a line through points O and P making sure that the line OP passes through the apparent center of the circle.
Where line MN and line OP intersect is the approximate center of the circle. Label this intersection point “Z.” If MN and OP do not intersect, extend each line until they do. Approximate the x,y coordinates of point Z in the form (x,y). In our example the coordinates for point Z were approximately (5,6).
The equation for a circle is (x-h)^2 + (y-k)^2=r^2 (^2 means "squared") where x is the x component of a point on the circle, y is the y component of a point on the circle, h is the x component of the center of the circle, k is the y component of the center of the circle, and r is the radius of the circle. In our example we will use point A (0,6) as the point on the circle, point Z (5,6) as the center of the circle. So in our equation x = 0, h = 5, y = 6, k = 6, and r is the variable. Our example equation would look like this: (0-5)^2 + (6-6)^2=r^2 .
Plug your approximate values into this equation, and using a little algebra you can solve for the radius of the circle. In our example we end up with r = 5.