A circle has a chord that goes from $pi/3$ to $pi/4$ radians on the circle. If the area of the circle is $49 pi$ , what is the length of the chord?

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Answer 1 · 2017-12-20T13:50:22

The length of the chord is $=1.83u$

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The angle subtended at the center of the circle is

$hat(AOB)=theta=pi/3-pi/4=pi/12$

The area of the circle is

$A=pir^2=49pi$

Therefore,

The radius of the circle is

$r=sqrt49=7$

The length of the chord is

$AB=2*AC=2*AOsin(theta/2)$

$=2*7*sin(pi/24)$

$=14*0.13$

$=1.83u$

A circle has a chord that goes from pi/3 pi/3 to pi/4 pi/4 radians on the circle. If the area of the circle is 49 pi 49 pi , what is the length of the chord?