A circle has a chord that goes from #( pi)/2 # to #(3 pi) / 4 # radians on the circle. If the area of the circle is #96 pi #, what is the length of the chord?

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Answer 1 · 2017-04-07T06:34:37

length of chord #~~ 7.499#

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Area of a circle #A=pir^2#,
Given #A=96pi, => r=sqrt96#

As shown in the figure, the angle #theta# subtended by the chord at the centre is :
#theta=(3pi)/4-pi/2=pi/4#
#=> theta/2=pi/8#

#=> AM=rsin(theta/2)#

#=># length of chord #AB=2AM=2*r*sin(theta/2)#
#= 2*sqrt96*sin(pi/8)~~7.499#