A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{5 π}{12}$ $(5 pi) / 12$ radians on the circle. If the area of the circle is $16 π$ $16 pi$ , what is the length of the chord?

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Answer 1 · 2017-03-01T08:49:14

length of chord $\approx 1.04$ $~~1.04$

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As area of a circle is given by $π r^{2}$ $pir^2$ and it is $16 π$ $16pi$ , we have $r = \sqrt{16} = 4$ $r=sqrt16=4$ .

As shown in the figure, the angle $Theta$ subtended at the centre by the chord is $(5pi)/12-pi/3=pi/12$

$=> AM=rsin(Theta/2)$
$=>$ length of chord $=AB=2AM=2rsin(Theta/2)$
$=2*4*sin(pi/24)=1.04$ (2dp)

A circle has a chord that goes from ( pi)/3 π3( pi)/3 to (5 pi) / 12 5π12(5 pi) / 12 radians on the circle. If the area of the circle is 16 pi 16π16 pi , what is the length of the chord?