Question

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

Answer 1

I found `28.3` units but have a look at my method.

Explanation:

I would first find the radius `r` as the distance between the center and your given point:
`r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt((4-1)^2+(2-2)^2)=sqrt(3^2+0^2)=3`

Then I would consider that the length `s` of an arc of angle `theta` (in radians) will be:
`s=r*theta`
so that:
`s=3*pi/4=3/4*3.14=28.27~~28.3` units