http://mathforum.org/dr.math/faq/faq.circle.segment.html#3
Segments of Circles:
The Arc, Chord, Radius, Height, Angle, Apothem, and Area
...
Case 3: You know s and h. Then solve
2h/s = (1-cos[x])/x,
for x, which must be done numerically (see below). Then
theta = 2x,
r = s/theta,
c = 2r sin(x),
d = r - h,
K = r2[theta-sin(theta)]/2.
Segments of Circles:
The Arc, Chord, Radius, Height, Angle, Apothem, and Area
...
Case 3: You know s and h. Then solve
2h/s = (1-cos[x])/x,
for x, which must be done numerically (see below). Then
theta = 2x,
r = s/theta,
c = 2r sin(x),
d = r - h,
K = r2[theta-sin(theta)]/2.
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