if a cord of length L is drawn... Let D be the distance from the center of the center of the circle to the cord. let the remaining distance to the edge of the circle be h. (such that r = D + h)

To get started, i think we need to obtain the equations for D and L

let theta be the central angle.

D = r*cos(.5*theta)

D = .5*L*cot(.5*theta)

D = .5(4*r^2-L^2)^.5


L = 2*r*sin(.5*theta)

L = 2*D*tan(.5*theta)

L = 2*(r^2-D^2)^.5

L = 2*[h*(2*r-h)]^.5


now, any ideas on what comes next???

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