A circle has a chord that goes from #( 5 pi)/4 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #42 pi #, what is the length of the chord?

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Answer 1 · 2017-09-07T11:09:28

The length of the chord is #7.89 # unit.

# (5*pi)/4 =225^0 and (5*pi)/3 =300^0 # .

The angle subtended at the center by the chord is

# c= 300-225=75^0# . The area of the circle is

#A_c=42*cancelpi = cancelpi *r^2 :. r^2 = 42 , r =sqrt 42#

We know , chord length # l_c = 2*r * sin (c/2) # or

#l_c= 2 *sqrt42 *sin (75/2) ~~ 7.89(2dp)# unit

The length of the chord is #7.89(2dp) # unit [Ans]