Question

A circle has a center at `(7 ,3 )` and passes through `(2 ,7 )`. What is the length of an arc covering `pi` radians on the circle?

Answer 1

`sqrt(41)pi`

Explanation:

If the circle has a center at `(7,3)` and passes through `(2,7)`
it has a radius of `r=sqrt((7-2)^2+(3-7)^2)=sqrt(41)`

The length of an arc covering `pi` radians is half the length of the circumference
`color(white)("XXX")(2pir)/2 = pir`

So in this case, the length of the arc is
`color(white)("XXX")pisqrt(41)`