Question

A circle's center is at `(7 ,4 )` and it passes through `(8 ,2 )`. What is the length of an arc covering `( pi ) /3` radians on the circle?

Answer 1

Length of the arc is `2.342`

Explanation:

As the circle's center is at `(7,4)` and it passes through `(8,2)`, its radius is given by distance between these two points and is equal to

`sqrt((8-7)^2+(2-4)^2)=sqrt(1^2+2^2)=sqrt5`

As length of an arc of a circle ofradius `r`, covering an angle `theta` (in radians) is given by `rtheta`

Length of the arc is `sqrt5xxpi/3=(2.23607xx3.14159)/3=2.342`