I'm afraid I don't understand what you're asking...? You say you found the gradients ("slopes", for American readers), but then you ask how to express the gradients...?
You have three points on the circle, and you have the general circle equation:
You could try plugging the three x,y-points into this equation, and then solving the resulting non-linear system for h, k, and r. But the method you've suggested may be easier.
Since points A and B lie on the horizontal line y = -1, their perpendicular bisector will be of the form x = (some number). So use the midpoint between A and B, and take the x-coordinate for your line equation.
You have found the midpoint of AC. To learn the relationship between the slopes of lines and their perpendiculars, try here. To learn how to find the line equation for the perpendicular bisector of AC from the slope and the midpoint, try here.
You should end up with the intersection of x = 3 and y = -x + 1 being the center (h, k) of your circle. Then the distance between the center and any of the three given points will give you the length r of the radius.