A circle's center is at $(2, 1)$ $(2 ,1 )$ and it passes through $(3, 7)$ $(3 ,7 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?

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Answer 1 · 2016-01-25T20:33:48

The arc length is $l = \frac{5 π}{12} \cdot \sqrt{37}$ $l=(5pi)/12*sqrt(37)$

First we have to calculate the length of the radius of the given circle.
The radius is equal to the distance between the given points:

$r = | A B | = \sqrt{{(3 - 2)}^{2} + {(7 - 1)}^{2}} = \sqrt{37}$ $r=|AB|=sqrt((3-2)^2+(7-1)^2)=sqrt(37)$

Now to calculate the arc length we have to multiply the angle in radians by the radius of the circle:

$l = \frac{5 π}{12} \cdot \sqrt{37}$ $l=(5pi)/12*sqrt(37)$

A circle's center is at (2,1)(2 ,1 ) and it passes through (3,7)(3 ,7 ). What is the length of an arc covering 5π12(5pi ) /12 radians on the circle?