A circle has a chord that goes from #pi/4 # to #pi/2 # 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 · 2017-10-16T10:50:12

The length of a 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 center by the chord. Area of circle is

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

#theta= pi/2-pi/4 = pi/4 :. L_c= 2 *4sqrt3 *sin ((pi/4)/2)# or

#L_c= 2 * 4sqrt3 * sin (pi//8) = 8 sqrt3 * sin 22.5 [pi/8=22.5^0] # or

#L_c= 5.30# unit. The length of a chord is # 5.30# unit.[Ans]