A chord with a length of $3$ $3$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-08-23T12:08:31

Area of the circle is $19.07$ $19.07$ sq.unit.

Chord length $L = 3$ $L= 3$ unit

Angle subtended at center by the chord is

$c = (\frac{π}{2} - \frac{π}{12}) = 90 - 15 = 75^{0}$ $c= (pi/2-pi/12)= 90-15=75^0$

We know chord length $L = 2 r sin (\frac{c}{2}); r$ $L = 2r sin (c/2) ;r$ is radius .

$:. 3 =2*r* sin (75/2) :. r = 3/ (2*sin37.5)~~2.464$ unit.

Area of the circle is $A_c= pi*r^2 = pi* (2.464)^2 ~~19.07$ sq.unit

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