Points (6 ,2 ) and (7 ,5 ) are (2 pi)/3 radians apart on a circle. What is the shortest arc length between the points?

1 Answer
sankarankalyanam
Feb 4, 2018

Shortest arc length s = R * theta = color(green)(3.8239

Explanation:

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Given theta = (2pi)/3 = 120^0#

c = sqrt((7-6)^2 + (5-2)^2) = 3.1623

r = c / (2 sin ((2pi)/6)) = 3.1623 / (2 * sin 60) = 1.8258

Shortest arc length s = R * theta = 1.8258 * ((2pi) / 3) = color(green)3.8239

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