(New page: 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 = ...) |
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D = r*cos(.5*theta) | D = r*cos(.5*theta) | ||
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D = .5*L*cot(.5*theta) | D = .5*L*cot(.5*theta) | ||
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D = .5(4*r^2-L^2)^.5 | D = .5(4*r^2-L^2)^.5 | ||
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L = 2*r*sin(.5*theta) | L = 2*r*sin(.5*theta) | ||
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L = 2*D*tan(.5*theta) | L = 2*D*tan(.5*theta) | ||
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L = 2*(r^2-D^2)^.5 | L = 2*(r^2-D^2)^.5 | ||
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L = 2*[h*(2*r-h)]^.5 | L = 2*[h*(2*r-h)]^.5 | ||
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now, any ideas on what comes next??? | now, any ideas on what comes next??? | ||
Latest revision as of 06:08, 5 October 2008
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???
