The perpendicular bisector of any chord on a circle passes through the circle's center. To find the center given three points, simply find the perpendicular bisectors of the first two and last two pairs of points and see where the bisectors intersect. After you find the center, calculate the distance from the center to one of the points to get the circle's radius.

If the bisectors do not intersect, the three points are colinear so they do not define a circle.

The following code shows how the program finds the circle defined by three points.

// Find a circle through the three points.
private void FindCircle(PointF a, PointF b, PointF c, out PointF center, out float radius)
{
    // Get the perpendicular bisector of (x1, y1) and (x2, y2).
    float x1 = (b.X + a.X) / 2;
    float y1 = (b.Y + a.Y) / 2;
    float dy1 = b.X - a.X;
    float dx1 = -(b.Y - a.Y);

    // Get the perpendicular bisector of (x2, y2) and (x3, y3).
    float x2 = (c.X + b.X) / 2;
    float y2 = (c.Y + b.Y) / 2;
    float dy2 = c.X - b.X;
    float dx2 = -(c.Y - b.Y);

    // See where the lines intersect.
    float cx = (y1 * dx1 * dx2 + x2 * dx1 * dy2 - x1 * dy1 * dx2 - y2 * dx1 * dx2)
        / (dx1 * dy2 - dy1 * dx2);
    float cy = (cx - x1) * dy1 / dx1 + y1;
    center = new PointF(cx, cy);

    float dx = cx - a.X;
    float dy = cy - a.Y;
    radius = (float)Math.Sqrt(dx * dx + dy * dy);
}