Question

A circle's center is at `(8 ,7 )` and it passes through `(6 ,5 )`. What is the length of an arc covering `(5 pi ) /6` radians on the circle?

Answer 1

`( 5 sqrt(2) pi ) / 3`

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius `r = sqrt( (6 - 8)^2 + (5 - 7)^2 ) = sqrt(2 * 2^2) = 2 sqrt(2)`.
Arc length `S = cancel(2) sqrt(2) * ( 5 pi ) / ( 3 cancel(6) ) = ( 5 sqrt(2) pi ) / 3`.