Points (2 ,2 ) and (8 ,1 ) are (5 pi)/3 radians apart on a circle. What is the shortest arc length between the points?

1 Answer
sankarankalyanam
Jan 10, 2018

Shortest arc length S = color (blue)(6.3699)

Explanation:

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W.r.t. the figure,

C = sqrt((8-2)^2 + (1-2)^2) = sqrt(37) = 6.0828

R = C / (2sin (theta/2)) = 6.0828 / (2 * sin((5pi)/6)) = 6.0828

To find the Shortest arc length, center angle will be

2pi - theta = 2pi - (5pi)/3 = pi / 3

S = R * theta =( 6.0828 * pi ) / 3 = 6.3699

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