A chord with a length of $18$ $18$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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A chord with a length of $18$ $18$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-12-23T05:55:59

Area of the circle is 685.6567

Explanation:

Chord length = 18
$θ = (\frac{π}{2}) - (\frac{π}{12}) = \frac{5 π}{12}$ $theta = (pi/2) - (pi/12) = (5pi) / 12$
$R = \frac{\frac{c}{2}}{sin (\frac{θ}{2})} = \frac{\frac{18}{2}}{sin (\frac{5 π}{24})} = 14.7841$ $R = (c/2) / sin (theta/2) = (18/2)/sin ((5pi)/24) = 14.7841$

Area of the circle = $π R^{2} = π \cdot {14.7841}^{2} = 685.6567$ $pi R^2 = pi* 14.7841^2 = 685.6567$

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A chord with a length of $18$ $18$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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Explanation:

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