Question

A circle's center is at `(2 ,4 )` and it passes through `(1 ,2 )`. What is the length of an arc covering `(5pi ) /12` radians on the circle?

Answer 1

Length of arc is `2.927`

Explanation:

As the center is at `(2,4)` and it passes through `(1,2)`,

the radius is distance between these two points or

`sqrt((1-2)^2+(2-4)^2)-sqrt(1+4)=sqrt5=2.236`

Now, in a circle if `r` is the radius and angle covered by an arc is `theta`, the length of arc is `rtheta` where `theta` is in radians.

Hence, considering `pi=3.1416` and `theta=(5pi)/12`

Length of arc is `(2.236xx5xx3.1416)/12` or `2.927`.