2
$\begingroup$

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?

1 Answers 1

3

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.

Edited:

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.

  • 0
    No, the angle is what I need to find. I know the radius however.2011-04-09
  • 0
    @Paul What *do* you know about the points? Their coordinates, or something else?2011-04-09
  • 0
    Their coordinates and the radius of the circle.2011-04-09
  • 0
    @Paul So, is my addition helpful?2011-04-09
  • 0
    Yes, thank you! :)2011-04-09