A circle has a chord that goes from #( 3 pi)/2 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #121 pi #, what is the length of the chord?

1 Answer
Yonas Yohannes
Mar 24, 2016

See geometric figure:
Chord, #bar(AB) = 11sqrt(2)#

enter image source here

Explanation:

This straight forward problem:
A) Determiner the radius from #C_A=piR^2#; #R =11#
Look at the angular displacement between #A ->B# it form
a right angle at the center so trangle AOB is an "isosceles right angle". Thus the ratio of side of an isosceles right triangle is:
#s_1:s_2:h=1:1:sqrt(2)# So for triangle AOD#=> a:f:bar(AD)=1:1:sqrt(2)#
#AD=11sqrt(2)/2#, thus the chord, #AB=11sqrt(2)#

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