How to find a circle with given two point with some point in a line?

The standard equation of a circle is (x-k)²+(y-h)²=r², (h,k) is center of the center, r is the radius. 
if the given two points form the diameter, find the midpoint of this diameter, the midpoint is the center of the circle. half the distance between these two points is the radius. 
you can also use the third point to find the radius, by plugging the x and y values into the equation after you find k and h. 

if either two of the three points form the diameter, plug the three different sets of x and y values in the equation. you have three equations with three unknown numbers h, k and r. solve to find h, k, and r.