A circle's center is at $(8 ,1 )$ and it passes through $(2 ,5 )$ . What is the length of an arc covering $(5 pi ) /6$ radians on the circle?

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Answer 1 · 2018-06-25T10:29:59

(8,1) and (2,5)

$d^2=(8-2)^2+(1-5)^2$

$d^2=36+16$

$d=sqrt 52$

The distance between the points is $sqrt53$ so the radius of the circle is $sqrt52$

Length of an arc is $theta/360xxpiD$

Where $theta$ is the angle of the arc and $D$ is the diameter of the circle.

$[5pi]/6=150^@$

Length= $150/360xxpixx2sqrt52$

Length is 18.87862233

A circle's center is at (8 ,1 )(8 ,1 ) and it passes through (2 ,5 )(2 ,5 ). What is the length of an arc covering (5 pi ) /6 (5 pi ) /6 radians on the circle?