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

1 Answer
Mar 11, 2016

=(2pisqrt5)/(3sqrt3)

Explanation:

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AB =sqrt((6-5)^2+(7-5)^2)=sqrt5
Let radius of circle =r
AB=AC+BC=rsin(pi/3)+rsin(pi/3)=2rsin(pi/3)=sqrt3r
r=(AB)/(sqrt3)=sqrt5/(sqrt3)

arc length = rxx(2pi/3)=sqrt5/(sqrt3)xx(2pi/3)=(2pisqrt5)/(3sqrt3)