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How can you find the length of the arc formed by two points on a circle? Is there any function that draws a perfect semi-circle so you can use integrals to find the value of the arc or is there a simpler solution?

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up vote 3 down vote accepted

Do you know the angle formed by those two points and the center of the circle? If so, and that angle is $\theta$ in radians, and the radius of the circle is $r$, then the arc length is $$ s = r \theta.$$

Read more here.


If you don't know $\theta$, you can find it by taking the dot product of the vectors from the center to each point. More on the dot product here.

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No, the angle is what I need to find. I know the radius however. – Paul Manta Apr 9 '11 at 7:26
@Paul What do you know about the points? Their coordinates, or something else? – Matthew Conroy Apr 9 '11 at 7:31
Their coordinates and the radius of the circle. – Paul Manta Apr 9 '11 at 7:40
@Paul So, is my addition helpful? – Matthew Conroy Apr 9 '11 at 7:49
Yes, thank you! :) – Paul Manta Apr 9 '11 at 7:50

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