The tangent at (3,3) has a slope of 2.
The line perpendicular to the tangent at (3,3) has a slope of -1/2.
The equation of this perpendicular is y = (9 -x)/2.
The chord from (1,1) to (3,3) has slope 1.
The equation of the perpendicular bisector of the chord (at (2,2) is y = 4 - x
The intersection of the perpendicular bisector of the cord and the perpendicular to the tangent is the center of the circle.
4 - x = (9 - x)/2
x = -1 and y = 5 is the center.
The radius is the distance from the center to (3,3) = sqrt(16 + 4) = 2√5
