Question

A circle's center is at `(8 ,3 )` and it passes through `(2 ,5 )`. What is the length of an arc covering `( pi ) /6` radians on the circle?

Answer 1

Length of the arc is `3.312` units.

Explanation:

As the circle's center is at `(8,3)` and it passes through `(2,5)`, its radius is the distance between two points i.e.

`sqrt((2-8)^2+(5-3)^2)=sqrt(36+4)=sqrt40=6.325`

Hence length of the arc covering angle `pi/6` is given by `rxxtheta`, where `r` is radius and `theta` angle in radians.

Hence, length of the arc is `6.325xxpi/6=(6.325xx3.1416)/6=3.312`