A circle has a chord that goes from $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $9 π$ $9 pi$ , 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 $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $9 π$ $9 pi$ , what is the length of the chord?

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Answer 1 · 2016-10-16T08:16:35

Length of chord is $6 sin (\frac{3 π}{8})$ $6sin((3pi)/8)$

Explanation:

Central angle $= \frac{17 π}{12} - \frac{2 π}{3} = \frac{17 π}{12} - \frac{8 π}{12} = \frac{9 π}{12} = \frac{3 π}{4}$ $=(17pi)/12-(2pi)/3=(17pi)/12-(8pi)/12=(9pi)/12=(3pi)/4$
Half central angle $= \frac{3 π}{8}$ $=(3pi)/8$
If area of circle is $9 π$ $9pi$ then we calculate the radius
$π r^{2} = 9 π$ $pir^2=9pi$ so $r^{2} = 9$ $r^2=9$ and $r = 3$ $r=3$
Length of chord = $2 r sin (\frac{θ}{2})$ $2rsin(theta/2)$ where $θ$ $theta$ is the central angle
So length of chord $= 2 \cdot 3 \cdot sin (\frac{3 π}{8}) = 6 sin (\frac{3 π}{8})$ $=2*3*sin((3pi)/8)=6sin((3pi)/8)$

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A circle has a chord that goes from $\frac{2 π}{3}$ $( 2 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $9 π$ $9 pi$ , what is the length of the chord?

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A circle has a chord that goes from 2π3( 2 pi)/3 to 17π12(17 pi) / 12 radians on the circle. If the area of the circle is 9π9 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 $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $9 π$ $9 pi$ , what is the length of the chord?