Question

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

Answer 1

arc length`=(11sqrt(2))/6` units

Explanation:

Let A`(2,1)` be the center of the circle and `B(3,2)` be the arc length.

Now, radius of circle`=AB=sqrt((3-2)^2+(2-1)^2)=sqrt(2)`

`rarrtheta=`arc length/(radius

`rarr=(7pi)/12=l/sqrt2`

`rarr7*(22/7)*1/12=l/sqrt(2)`

`rarrl=(11sqrt2)/6` units