Question

A circle's center is at `(7 ,2 )` and it passes through `(5 ,8 )`. What is the length of an arc covering `(7pi ) /4` radians on the circle?

Answer 1

`=34.76`

Explanation:

So the distance between points `(7,2)` and `(5,8)` is the radius of the circle.
So the distance is
`=sqrt((7-5)^2+(8-2)^2`
`=sqrt(2^2+6^2)`
`=sqrt(4+36)`
`=sqrt40`
`=6.32`
Therefore radius of the Circle `r=6.32`
The Circumference of the circle`=2pir=2pi(6.32)=39.73`
An Arc covers `7pi/4` radians
or
It covers `7pi/4-:2pi=7/8` of the Circumference
Therefore; Length of the Arc`=7/8(39.73)=34.76`