Question

A circle has a chord that goes from `( 3 pi)/4` to `(5 pi) / 4` radians on the circle. If the area of the circle is `72 pi`, what is the length of the chord?

Answer 1

Length of the chord`" "l=12" "`units

Explanation:

The central angle `theta=(5pi)/4-(3pi)/4=pi/2`
We have a triangle with sides `r, r, l` and angle `theta` opposite side `l`

Area of the circle `A=pir^2`
`A=72pi` is given

Area = Area
`72pi=pi r^2`
`r^2=72`
`r=6sqrt2`

By the cosine law we can solve for the length `l`

`l=sqrt((r^2+r^2-2*r*r*cos theta))`
`l=sqrt((72+72-2*72*cos (pi/2)))`
`l=sqrt144`
`l=12" "`units

God bless....I hope the explanation is useful.