y-length of a circular arc

OB = 1
OC = L
OD = b

y-length of the circular arc OC, relative to O:

y-length = 1 - (1 - L²)^½

y-length of the circular arc DC, relative to O:

y-length = (1 - b²)^½ - (1 - L²)^½

if C and D are an equal distance along the circular arc from Q:

y-length = L - b

in the diagram:
OB = 1
OC = .9
OD = .56

y-length of the arc OC, relative to O, is

1 - (1 - .9²)^½
= .564110

y-length of the arc DC, relative to O, is

[1 - (.56)²]^½ - [1 - (.9)²]^½
= .828492 - .435889
= .392602