Points $(2 ,9 )$ and $(1 ,5 )$ are $(3 pi)/4$ radians apart on a circle. What is the shortest arc length between the points?

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Answer 1 · 2017-07-12T09:39:47

The arc length is $=5.26$

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The angle $theta=3/4pi$

The distance between the points is

$d=sqrt((2-1)^2+(9-5)^2)$

$=sqrt(1+16)$

$=sqrt17$

This is the length of the chord

So,

$d/2=rsin(theta/2)$

$r=d/(2sin(theta/2))$

$=sqrt17/(2sin(3/8pi))$

$=2.23$

The length of the arc is

$L=rtheta=2.23*3/4pi=5.26$

Points (2 ,9 )(2 ,9 ) and (1 ,5 )(1 ,5 ) are (3 pi)/4 (3 pi)/4 radians apart on a circle. What is the shortest arc length between the points?