Question

A circle's center is at `(5 ,9 )` and it passes through `(7 ,3 )`. What is the length of an arc covering `(15pi ) /8` radians on the circle?

Answer 1

`(15sqrt10pi)/4~~37.25` units

Explanation:

Given circle's center `O` is at `(5,9)` and the circle passes through `(7,3)`,
`=>` radius of the circle `r=sqrt((7-5)^2+(3-9)^2)=sqrt(4+36)=sqrt40`

Arc length `=rtheta` (`theta` in radians)
given `theta=(15pi)/8`,
arc length `= sqrt40xx(15pi)/8=2sqrt10xx(15pi)/8`
`=(15sqrt10*pi)/4~~37.25` units