Here is the process you should follow:

First, find the equations of two line that pass through 2 point (for example, one line that passes through P1 and P2; and a second one that passes through P2 and P3) say L1, and L2, then find the slope of each line, and the midpoint between the points that it passes.

Now, find the equation of the perpendicular line to L1 and L2 that passes through the midpoint you found earlier, and lets call those M1, and M2.

Find the intersection point of M1 and M2, and thats the center of your cirlce, say C. Now just find the distance from C to P1, P2 or P3 and thats your radius.

Now the equation of the circle is (x-c1)²+(y-c2)²=r² where C=(c1,c2) and r is the radius.