Question

Points `(5 ,2 )` and `(1 ,4 )` are `(2 pi)/3` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

Shortest arc length `s = color (blue)5.4077`

Explanation:

Chord length `l_c = sqrt((1-5)^2 + (4-2)^2) = 4.4721`

`r = l_c / 2sin(theta/2) = 4.4721/(2*sin (pi/3)) = 2.582`

Arc length `s = r theta = 2.582 * ((2pi)/3) = color (blue)(5.4077)`