A circle has a chord that goes from $( 2 pi)/3$ to $(11 pi) / 12$ radians on the circle. If the area of the circle is $48 pi$ , what is the length of the chord?

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Answer 1 · 2017-12-05T10:56:26

The length of the chord is $5.30$ unit.

Formula for the length of a chord is $L_c= 2r sin (theta/2)$

where $r$ is the radius of the circle and $theta$ is the angle

subtended at the centre by the chord. Area of circle is

$cancelpi * r^2 = 48 cancelpi :. r^2 = 48 or r = sqrt48 =4 sqrt3$

$theta= (11pi)/12-(2pi)/3 = (3pi)/12=pi/4=45^0$

$:. L_c= 2 *4sqrt3 *sin (45/2)$ or

$L_c= 2 * 4sqrt3 * sin22.5 ~~ 5.3$ unit.

The length of the chord is $5.30$ unit.[Ans]

A circle has a chord that goes from ( 2 pi)/3 ( 2 pi)/3 to (11 pi) / 12 (11 pi) / 12 radians on the circle. If the area of the circle is 48 pi 48 pi , what is the length of the chord?