A circle has a chord that goes from #( 3 pi)/4 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #72 pi #, what is the length of the chord?

1 Answer
Leland Adriano Alejandro
Mar 24, 2016

Length of the chord#" "l=12" "#units

Explanation:

The central angle #theta=(5pi)/4-(3pi)/4=pi/2#
We have a triangle with sides #r, r, l# and angle #theta# opposite side #l#

Area of the circle #A=pir^2#
#A=72pi# is given

Area = Area
#72pi=pi r^2#
#r^2=72#
#r=6sqrt2#

By the cosine law we can solve for the length #l#

#l=sqrt((r^2+r^2-2*r*r*cos theta))#
#l=sqrt((72+72-2*72*cos (pi/2)))#
#l=sqrt144#
#l=12" "#units

God bless....I hope the explanation is useful.

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