hello :
an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a = (3+2)/2 = 5/2 and b = (1+1)/2 =1
let : B(3;1) and ; C (2,1)
r = BC/2
BC = √(3-2)²+(1-1)² ) =1
r = 1/2
the equation for the circle is : (x-5/2)² +(y-1)² = 1/4