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 $48 π$ $48 pi$ , what is the length of the chord?

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Answer 1 · 2017-05-27T08:09:48

$s = π \frac{\sqrt{3}}{3} u n i t s$ $s=pisqrt3/3 units$

The length of a chord is given by

$s = r θ$ $s=rtheta$

where: $r = the radius of the circle$ $" "r=" the radius of the circle"$

and, $θ =$ $" "theta " = "$ angle subtended - in RADIANS- by the chord at the centre of the circle

1) find the radius with the given information

$A_{c} = π r^{2}$ $A_c=pir^2$

$48cancel(pi)=cancel(pi)r^2$

$:.r=sqrt48=4sqrt3$

2) find the angle $theta$

$theta=(5pi)/12-pi/3=(5pi)/12-(4pi)/12=pi/12$

3) find the arc length

$s=cancel(4)sqrt3xxpi/cancel(12)^3$

$s=pisqrt3/3$

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 48 pi 48π48 pi , what is the length of the chord?