Question

A circle has a chord that goes from `( pi)/2` to `(3 pi) / 4` radians on the circle. If the area of the circle is `196 pi`, what is the length of the chord?

Answer 1

`~~ 10.72`

Explanation:

`• " the area of a circle "=pir^2`

`rArrpir^2=196pi`

`rArrr^2=(196cancel(pi))/cancel(pi)=196`

`rArrr=sqrt196=14`

`"the angle subtended at the centre of the circle by the"`
`"chord is"`

`(3pi)/4-pi/2=(3pi)/4-(2pi)/4=pi/4`

`"we now have a triangle made up of the 2 radii and the"`
`"chord "`

`"to find length of chord use the "color(blue)"cosine rule"`

`•color(white)(x)c^2=a^2+b^2-2abcosC`

`"where "a=b=14" and "angleC=pi/4`

`c^2=14^2+14^2-(2xx14xx14xxcos(pi/4))`

`color(white)(c^2)~~ 114.814`

`rArrc=sqrt114.814~~ 10.72" to 2 dec. places"`

`rArr"length of chord "~~ 10.72`