Question

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

Answer 1

The arc length is `l=(5pi)/12*sqrt(37)`

Explanation:

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=|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=(5pi)/12*sqrt(37)`