I need a simplest and 100% correct formula (or method) to find equation of a circle with 3 points given.
Given that , , and are points on the plane, then and are midpoints of chords in the circle. The two chords have slopes and respectively so that and are the slopes of the perpendicular lines.
That means that and are equations of the radii through the midpoints and so intersect the center, . Solve those two equations simultaneously to find and . Of course, once you have that, the radius of the circle is given by and then the equation of the circle is .