A circle has a chord that goes from $( 3 pi)/2$ to $(7 pi) / 4$ radians on the circle. If the area of the circle is $144 pi$ , what is the length of the chord?

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Answer 1 · 2016-03-25T02:47:58

Length of the chord $l=12sqrt(2-sqrt2)=9.18440237676$

Area $=pi r^2=144 pi$

therefore $r^2=144$

and $r=12$

$l=sqrt(r^2+r^2-2*r*r*cos ((7 pi)/4-(3pi)/2)$

$l=sqrt(144+144-2*144*cos (pi/4))$

$l=sqrt(288-2*144*(1/sqrt2))$

$l=12sqrt(2-sqrt2)=9.18440237676$

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

A circle has a chord that goes from ( 3 pi)/2 ( 3 pi)/2 to (7 pi) / 4 (7 pi) / 4 radians on the circle. If the area of the circle is 144 pi 144 pi , what is the length of the chord?