Points (6 ,7 ) and (7 ,5 ) are (2 pi)/3 radians apart on a circle. What is the shortest arc length between the points?
1 Answer
Feb 17, 2016
Explanation:
Refer to the figure below
I created this figure using MS Excel
Or
Applying Law of Cosines in
AB^2=r^2+r^2-2r*r*cos 180^@
2r^2-2r^2*(-1/2)=(sqrt(5))^2
3r^2=5 =>r=sqrt(5/3)
Length of the arc
arc AB=r*alpha , where alpha is given in radians
arc AB=sqrt(5/3)*(2*pi)/3*(sqrt(3)/sqrt(3))=2/9*sqrt(15)*pi