A circle has a chord that goes from #( 2 pi)/3 # to #(11 pi) / 12 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?

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Answer 1 · 2017-12-05T10:56:26

The length of the chord is # 5.30# unit.

Formula for the length of a chord is #L_c= 2r sin (theta/2)#

where #r# is the radius of the circle and #theta# is the angle

subtended at the centre by the chord. Area of circle is

# cancelpi * r^2 = 48 cancelpi :. r^2 = 48 or r = sqrt48 =4 sqrt3#

#theta= (11pi)/12-(2pi)/3 = (3pi)/12=pi/4=45^0#

# :. L_c= 2 *4sqrt3 *sin (45/2)# or

#L_c= 2 * 4sqrt3 * sin22.5 ~~ 5.3 # unit.

The length of the chord is # 5.30# unit.[Ans]