A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $96 π$ $96 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $96 π$ $96 pi$ , what is the length of the chord?

1 Answer

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Answer 1 · 2016-10-18T11:54:03

Lengthof chord $= 4 \sqrt{6}$ $=4sqrt6$

Explanation:

From the area, we calculate the radius $r^{2} π = 96 π$ $r^2pi=96pi$
so $r^{2} = 96$ $r^2=96$ and $r = 4 \sqrt{6}$ $r=4sqrt6$
The angle at the center is $θ = \frac{2 π}{3} - \frac{π}{3} = \frac{π}{3}$ $theta=(2pi)/3-pi/3=pi/3$
The length of the chord is $2 r sin (\frac{θ}{2}) = 2 \cdot 4 \sqrt{6} \cdot \frac{sin π}{6} = \frac{8 \sqrt{6}}{2} = 4 \sqrt{6}$ $2rsin(theta/2)=2*4sqrt6*sin pi/6=(8sqrt6)/2=4sqrt6$

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A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $96 π$ $96 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from π3( pi)/3 to 2π3(2 pi) / 3 radians on the circle. If the area of the circle is 96π96 pi , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{2 π}{3}$ $(2 pi) / 3$ radians on the circle. If the area of the circle is $96 π$ $96 pi$ , what is the length of the chord?