Question 122054
I'm just going to tell you what you need to do.  If you still can't figure it out after that, write back.


Label your points {{{P[1]}}}, {{{P[2]}}}, and {{{P[3]}}}.


Use the two-point form of the straight line to create the equation for the line containing {{{P[1]}}} and {{{P[2]}}}, to obtain the slope of the line.  The segment {{{P[1]P[2]}}} forms a chord of the desired circle.  A perpendicular to a chord passing through the mid-point of the chord passes through the center of the circle.  Determine the mid-point of {{{P[1]P[2]}}} using the mid-point formula:  {{{x[m]=(x[1]+x[2])/2}}} and {{{y[m]=(y[1]+y[2])/2}}}.  Recalling that slopes of perpendicular lines are negative reciprocals, create the equation of the perpendicular to the chord that passes through the calculated mid-point.


Then do the same thing for {{{P[2]}}} and {{{P[3]}}}.


Now you have two linear equations in two variables that we know intersect at the circle's center.  Solve the system of equations to determine the circle center, (h, k).


Once you determine the center point, use the distance formula to find the distance between the center and any one of your given points.  That will be the circle radius, r.


Your equation will then be {{{(x-h)^2+(y-k)^2=r^2}}}