A chord with a length of $6$ runs from $pi/3$ to $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2016-03-01T12:59:30

$412.53$

As the chord with a length of $6$ runs from $pi/3$ to $pi/2$ radians, it is obvious that it subtends an angle of $pi/2-pi/3=pi/6$ .

Hence, the chord subtends an angle of $pi/6$ at center. Hence complete circumference, which subtends an angle of $2pi$ should be of length

$6xx(2pi)/(pi/6)=6xx2pixx6/pi$ i.e. $72$ .

Hence, radius of circle is $72/(2pi)=36/pi$ , and area of circle will be

$pixx(36/pi)^2=36xx36/pi=412.53$

A chord with a length of 6 6 runs from pi/3 pi/3 to pi/2 pi/2 radians on a circle. What is the area of the circle?