A chord with a length of $1$ runs from $pi/8$ to $pi/3$ radians on a circle. What is the area of the circle?

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Answer 1 · 2018-01-18T12:30:14

Area of the circle $A_c = pi r^2 = pi (1.5555)^2 = color(brown)(7.6013)$ sq. units

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$/_(AOM) = theta = (pi/3) - (pi/8) = ((5pi)/24)$

$theta / 2 = ((5pi)/48)$

Length of chord $= AB = L_c = 1$ Given

$OA = r = (L_c / 2)* (1 / sin (theta/2)) =( 1/2) * (1/ sin ((5pi)/48))$

$r = 1.5555 units$

Area of the circle $A_c = pi r^2 = pi (1.5555)^2 = color(brown)(7.6013)$ sq. units

A chord with a length of 1 1 runs from pi/8 pi/8 to pi/3 pi/3 radians on a circle. What is the area of the circle?