A circle has a chord that goes from #( pi)/3 # to #(5 pi) / 12 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?

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Answer 1 · 2017-05-27T08:09:48

#s=pisqrt3/3 units#

The length of a chord is given by

#s=rtheta#

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

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

1) find the radius with the given information

#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#