A circle has a chord that goes from $( 11 pi)/6$ to $(7 pi) / 4$ radians on the circle. If the area of the circle is $120 pi$ , what is the length of the chord?

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Answer 1 · 2017-06-07T13:27:26

The length of the chord is $=2.86$

The area of the circle is $=120pi$

Let the radius of the circle be $=r$

Then,

$pir^2=120pi$ , $=>$ , $r^2=120$ , $r=sqrt120$

The angle subtended by the chord at the centre of the circle is

$theta=11/6pi-7/4pi=44/24pi-42/24pi=2/24pi=1/12pi$

The length of the chord is

$=2rsin(theta/2)=2*sqrt120sin(1/2*1/12pi)$

$=2.86$

A circle has a chord that goes from ( 11 pi)/6 ( 11 pi)/6 to (7 pi) / 4 (7 pi) / 4 radians on the circle. If the area of the circle is 120 pi 120 pi , what is the length of the chord?