Question

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

Answer 1

`=12.4`

Explanation:

Circle's center is at `(2,5)` and it passes through `(1,2)`
Therefore Length of the `radius=r` =Distance between these points`(2,5) and (1,2)`
or
`radius =r=sqrt((2-1)^2+(5-2)^2)`
`=sqrt(1^2+3^2)`
`=sqrt(1+9)`
`=sqrt10`
`=3.16`
Therefore Circumfernce of the Circle `=2pir=2pitimes3.16~=19.87`
Arc covers `(5pi)/4` radians on the Circle
In other words Arc covers `(5pi)/4-:2pi=5/8times`(circumference of the Circle)
Therefore Length of the Arc `=5/8 times2pir=5/8 times19.87~=12.4`