A circle has a chord that goes from ( 5 pi)/4 to (5 pi) / 3 radians on the circle. If the area of the circle is 42 pi , what is the length of the chord?

1 Answer
Binayaka C.
Sep 7, 2017

The length of the chord is 7.89 unit.

Explanation:

(5*pi)/4 =225^0 and (5*pi)/3 =300^0 .

The angle subtended at the center by the chord is

c= 300-225=75^0 . The area of the circle is

A_c=42*cancelpi = cancelpi *r^2 :. r^2 = 42 , r =sqrt 42

We know , chord length l_c = 2*r * sin (c/2) or

l_c= 2 *sqrt42 *sin (75/2) ~~ 7.89(2dp) unit

The length of the chord is 7.89(2dp) unit [Ans]

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