Question

A circle has a center at `(1 ,3 )` and passes through `(2 ,4 )`. What is the length of an arc covering `pi` radians on the circle?

Answer 1

`4.44` units

Explanation:

The radius of the circle is the distance between the centre and the given point.

`r=d((1,3);(2,4))=sqrt((2-1)^2+(4-3)^2)=sqrt2`

So the equation of this circle is `(x-1)^2+(y-3)^2=2`.

An arc length covering `pi` radians (`180^@`) is effectively half the circumference of the circle, ie
`1/2xx2pir`

`=1/2xx2xxpixxsqrt2`

`=pisqrt2` units

`=4.44` units.