A chord with a length of 12 runs from pi/12 to pi/8 radians on a circle. What is the area of the circle?

1 Answer
Jul 28, 2017

The area of the circle is =26439.6u^2

Explanation:

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The angle subtended at the centre of the circle is

hat(AOB)=theta=pi/8-pi/12=3/24pi-2/24pi=1/24pi

The length of the chord is

AB=12

AC=12/2=6

sin(theta/2)=(AC)/r

The radius of the circle is

r=(AC)/sin(theta/2)=6/sin(1/2*1/24pi)=6/sin(1/48pi)=91.7u

The area of the circle is

area=pir^2=pi*91.7^2=26439.6u^2