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

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Answer 1 · 2018-07-15T01:57:21

$color(crimson)("Length of the chord " bar(AB) ~~ 6.0147$

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$"Area of circle " = A_c = 16 pi$

$"Radius " = bar (OA) = r = sqrt ((16 pi) / (pi)) = 4$

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

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 ( pi)/3 to (7 pi) / 8 (7 pi) / 8 radians on the circle. If the area of the circle is 16 pi 16 pi , what is the length of the chord?