A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ to $\frac{7 π}{8}$ $(7 pi) / 8$ radians on the circle. If the area of the circle is $16 π$ $16 pi$ , what is the length of the chord?

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Answer 1 · 2018-07-15T01:57:21

$Length of the chord ¯ ¯¯¯¯ ¯ A B \approx 6.0147$ $color(crimson)("Length of the chord " bar(AB) ~~ 6.0147$

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$Area of circle = A_{c} = 16 π$ $"Area of circle " = A_c = 16 pi$

$Radius = ¯ ¯¯¯¯ ¯ O A = r = \sqrt{\frac{16 π}{π}} = 4$ $"Radius " = bar (OA) = r = sqrt ((16 pi) / (pi)) = 4$

$"Given ' hat (AOB) = (7pi) / 8 - pi / 3 = (13pi ) / 24$

To fin $bar(AB)$

$"In "Delta AOM, (AM) = (AO) * sin (AOM)$

$bar (AB) = 2 * bar (AM)$

$:. bar (AB) = bar (AO) * (2 * sin (AOM) )$

$color(crimson)(bar(AB) = 4 * 2 * sin ((13pi)/48) = 6.0147$

A circle has a chord that goes from ( pi)/3 π3( pi)/3 to (7 pi) / 8 7π8(7 pi) / 8 radians on the circle. If the area of the circle is 16 pi 16π16 pi , what is the length of the chord?