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

1 Answer
sankarankalyanam
Jan 7, 2018

Shortest arc length s = color (blue)5.4077

Explanation:

enter image source here
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)

Related questions
See all questions in Circle Arcs and Sectors
Impact of this question
1978 views around the world
You can reuse this answer
Creative Commons License