A chord with a length of $5$ runs from $pi/12$ to $pi/6$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-07-27T08:28:35

The area of the circle is $=1152.5u^2$

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The angle subtended at the centre of the circle is

$hat(AOB)=theta=pi/6-pi/12=2/12pi-1/12pi=1/12pi$

The length of the chord is

$AB=5$

$AC=5/2=2.5$

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

The radius of the circle is

$r=(AC)/sin(theta/2)=2.5/sin(1/2*1/12pi)=2.5/sin(1/24pi)=19.2u$

The area of the circle is

$area=pir^2=pi*19.2^2=1152.5u^2$

A chord with a length of 5 5 runs from pi/12 pi/12 to pi/6 pi/6 radians on a circle. What is the area of the circle?