Circular segment: Difference between revisions

Revision as of 16:18, 17 April 2022

Revision as of 17:32, 17 April 2022

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The chord length is

:<math>c =2\sqrt{2hR-h^2}= 2R\sin\tfrac{\theta}{2} = R\sqrt{2(1-\cos\theta)}</math>

:<math>c = 2\sqrt{R^2 - (R - h)^2} = 2\sqrt{2Rh - h^2}</math>

The sagitta is

:<math>h =R-\sqrt{R^2-\frac{c^2}{4}}= R(1-\cos\tfrac{\theta}{2})=R\left(1-\sqrt{\tfrac{1+\cos\theta}{2}}\right)=\frac{c}{2}\tan\frac{\theta}{4}</math>