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

1 Answer
Harish Chandra Rajpoot
Jul 26, 2018

2.342\ \text{ unit

Explanation:

The distance d between the given points (5, 2) & (4, 4) is

d=\sqrt{(5-4)^2+(2-4)^2}

=\sqrt{5}

Now, the radius R of circle is given as

\sin ({5\pi}/6)=\frac{d/2}{R}

\sin(\pi/6)=d/{2R}

1/2=\sqrt5/{2R}

R=\sqrt5

hence, the shortest arc length between given points which are {5\pi}/3 apart

=(2\pi-{5\pi}/3)R

=\pi/3(\sqrt5)

=2.342\ \text{ unit

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