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#