A chord with a length of $5$ runs from $pi/8$ to $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-08-03T11:29:15

The area of the circle is 63.62 # sq.unit.

Formula for chord length is $C_l = 2*r * sin (c/2)$ , where $c$ is the

angle subtended at the centre by the chord and $r$ is the radius of

the circle. Here $C_l=5 , c= (pi/2 -pi/8) = 180/2 - 180/8$

$=90-22.5 = 67.5^0 ; r = C_l/(2*sin(c/2)) = 5/(2*sin 33.75)$ or

$r = 5/1.11 ~~ 4.5$ .

The area of the circle is $A=pi*r^2 = pi* 4.5^2 ~~ 63.62$ sq.unit

[Ans]

A chord with a length of 5 5 runs from pi/8 pi/8 to pi/2 pi/2 radians on a circle. What is the area of the circle?