A circle has a chord that goes from #pi/12 # to #pi/4 # radians on the circle. If the area of the circle is #14 pi #, what is the length of the chord?

1 Answer
CW
Mar 18, 2017

length of chord #=sqrt7(sqrt3-1)~~1.9368#

Explanation:

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As area of a circle is given by #pir^2#, and it is #14pi#, we have #r=sqrt14#.

As shown in the figure, the angle #Theta# subtended by the chord at the centre is :
#Theta=pi/4-pi/12=pi/6#
#=> Theta/2=pi/12#

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

#=># length of chord #AB=2AM=2*r*sin(Theta/2)#
#= 2*sqrt14*sin(pi/12)~~1.9368#

exact value:
#=2*sqrt14*((sqrt6-sqrt2)/4)#
=#sqrt21-sqrt7=sqrt7(sqrt3-1)#

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