A circle has a chord that goes from $pi/4$ to $pi/8$ 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 · 2018-04-18T06:14:54

$color(purple)("Length of Chord " d = 2r sin theta ~~ 5.3 " units"$ #

Given $" Area = 48 pi, theta = pi / 4 - pi/ 8 = pi / 8$

![http://www.engineeringexpert.net/Engineering-Expert-Witness-Blog/determining-chord-length-on-circle-earth]( useruploads.socratic.org )

$"Chord length " d = 2r * sin theta$

Given $"Area of circle " = pi r^2 = 48pi$

$r = sqrt46 = 4 sqrt3$

$"Length of Chord " d = 2r * sin theta = 2 * 4 sqrt 3 * sin (pi / 8)$

$color(purple)(d = 8 sqrt 3 sin (pi/8) ~~ 5.3 " units"$ #

A circle has a chord that goes from pi/4 pi/4 to pi/8 pi/8 radians on the circle. If the area of the circle is 48 pi 48 pi , what is the length of the chord?