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The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. Either of the two regions into which a secant or a chord cuts a circle. (However, the formulas below assume that the segment is no larger than a semi-circle.)
Chord length: c
Height: h
Distance from center of circle to chord's midpoint: d
Central angle: theta (in radians), alpha (in degrees)
Area: K
Arc length: s
theta = 2 arccos(d/r) = 2 arctan(c/(2d)) = 2 arcsin(c/(2r))
h = r - d
c = 2 sqrt(r2-d2) = 2r sin(theta/2) = 2d tan(theta/2) = 2 sqrt[h(2r-h)]
d = sqrt(4r2-c2)/2 = r cos(theta/2) = c cot(theta/2)/2
K = r2[theta-sin(theta)]/2 = r2arccos([r-h]/r) - (r-h)sqrt(2rh-h2)
= r2arccos(d/r) - d sqrt(r2-d2)
theta = s/r
K = r2[s/r - sin(s/r)]/2
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