A chord with a length of $1$ $1$ 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 $1$ $1$ 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 · 2018-02-13T03:11:55

Area of the circle $A_{c} = \approx 28.2743$ $A_c =color(green)(~~ 28.2743$ sq units

Explanation:

enter image source here
In the figure above,

$A ˆ O B = θ = \frac{π}{2} - \frac{π}{12} = \frac{5 π}{12}, A M = \frac{A B}{2} = \frac{1}{2}$ $AhatOB = theta = pi/2 - pi/12 = (5pi)/12, AM = (AB) / 2 = 1/2$

$- - \to O A = r = \frac{A M}{sin (\frac{θ}{2})} = \frac{\frac{1}{2}}{sin (\frac{5 π}{24})} \approx 0.3$ $vec(OA) = r = (AM) / sin (theta/2) = (1/2) / sin ((5pi)/24) ~~ 0.3$

Area of the circle $A_{c} = π r^{2} = π \cdot 3^{2} = \approx 28.2743$ $A_c = pi r^2 = pi * 3^2 = color(green)(~~ 28.2743$ sq units

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A chord with a length of $1$ $1$ 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 $1$ $1$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?