Here's one way to solve this....but....maybe not the fastest....!!!!
Let D =(0,0) E = (0, 1/2) B =(1.1) C = (1,0)
Call the center of the circle ( m, 1/2)
So the distances from each of these points to the center are equal = the radius
We have this
Distance from center to E = distance from center to B
( m - 0)^2 + ( 1/2 - 1/2)^2 = ( m - 1)^2 + ( 1/2 -1)^2
m^2 = m^2 - 2m + 1 + 1/4
2m = 5/4
m = 5/8
So the radius = the distance from (m,n) to E =
sqrt [ 0 - 5/8)^2 + ( 1/2 - 1/2)^2 ] =
sqrt[ ( 5/8 )^2 ] =
5/8