Question

A circle has a center at `(7 ,9 )` and passes through `(1 ,1 )`. What is the length of an arc covering `(3pi ) /4` radians on the circle?

Answer 1

`(15pi)/2`

Explanation:

First thing to do is to find the length of the radius. The line segment joining the center of the circle to <b>any</b> point on the circle constitutes a radius.

Therefore, the line segment joining `(7,9)` and `(1,1)` is a radius. To find its length, you can use Pythagoras Theorem.

`r = sqrt{(7 - 1)^2 + (9 - 1)^2} = 10`

Next, you should know that an arc subtending an angle of `theta` in radians, has arc length, s, given by `s = r theta`.

`s = (10)*((3pi)/4) = (15pi)/2`