A chord with a length of $16$ runs from $pi/3$ to $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-12-21T15:15:50

Area of the circle = 13.4692

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Given $/_(AOB )= pi/2 - pi/3 = (pi)/6$

$/_ (AOM) = /_ (AOB) / 2 = ((pi)/6) / 2 = (pi)/12$

$AB = 16, :. AM = 16/2 = 8$

Radius $OA = r = AM * sin /_AOM = 8 * sin ((pi)/12)$

Radius $r = 2.0706$

$Area = pi r^2 = pi * (2.0706)^2 = 13.4692$

A chord with a length of 16 16 runs from pi/3 pi/3 to pi/2 pi/2 radians on a circle. What is the area of the circle?