Area under Arc of Circle
Date: 02/27/2001 at 18:29:32 From: Michelle Drapeau Subject: Area under arc of circle Dear Dr. Math, I would like to calculate the area delimited by the arc of a circle and the chord of that arc when (this is the important part) all I have is the length of the chord and the length of a line perpendicular to the chord and running from the middle of the chord to the edge of the circle (noted as letter h in the archive section 'segments of circles'). Segments of Circles - Dr. Math FAQ http://mathforum.org/dr.math/faq/faq.circle.segment.html All formulas I have found, including the ones found on the above FAQ page, require either theta (or alpha) or the radius, I have neither. Thank you for your help, Michelle
Date: 02/27/2001 at 23:19:04 From: Doctor Peterson Subject: Re: Area under arc of circle You have h and c. The FAQ gives these formulas: K = r^2[theta-sin(theta)]/2 = r^2 arccos([r-h]/r) - (r-h)sqrt(2rh-h^2) = r^2 arccos(d/r) - d sqrt(r^2-d^2) What you missed is that the FAQ also tells you how to find c given h and r: c = ... = 2 sqrt[h(2r-h)] You can solve this to find r in terms of c and h, the values you have: c^2 + 4h^2 r = ---------- 8h Now plug that into the equation for K in terms of r and h, and you'll have what you need. It will be horribly ugly, but it works! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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