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?
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.