A circle has a chord that goes from #pi/4 # to #(3 pi) / 8 # radians on the circle. If the area of the circle is #81 pi #, what is the length of the chord?

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Answer 1 · 2017-11-17T11:28:20

The length of the chord is # 3.51# 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 = 81 cancelpi :. r^2 = 81 or r = sqrt81 =9.0#

#theta= (3pi)/8-pi/4 = pi/8 :. L_c= 2 *9 *sin ((pi/8)/2)# or

#L_c= 18 * sin (pi/16) ~~ 3.51 (2dp) orL_c ~~ 3.51 (2dp)# unit.

The length of the chord is # 3.51# unit.[Ans]