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

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

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Answer 1 · 2016-08-06T09:27:51

$= 2.72$ $=2.72$

Explanation:

A chord that goes from $2 \frac{π}{3}$ $2pi/3$ to $11 \frac{π}{12}$ $11pi/12$
so it travels the distance $11 \frac{π}{12} - 2 \frac{π}{3} = \frac{π}{4}$ $11pi/12-2pi/3=pi/4$ ;
or
$\frac{π}{4} \div 2 π = \frac{1}{8}$ $pi/4-:2pi=1/8$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 12 π$ $=pir^2=12pi$
or
$r^{2} = 12$ $r^2=12$
or
$r = \sqrt{12}$ $r=sqrt12$
or
$r = 3.46$ $r=3.46$
Circumference of the circle $= 2 π r = 2 (π) (3.46) = 21.77$ $=2pir=2(pi)(3.46)=21.77$
Therefore Length of the chord $= \frac{21.77}{8} = 2.72$ $=21.77/8=2.72$

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

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