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A chord with a length of $2$ $2$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

1 Answer

Feb 26, 2016

$Area = π \cdot {(csc (\frac{π}{8}))}^{2}$ $"Area" = pi*(csc(pi/8))^2$

Explanation:

From the diagram (below) we note that the radius of the circle is
$XXX r = csc (\frac{π}{8})$ $color(white)("XXX") r=csc(pi/8)$

enter image source here

So the area is
$XXX Area = π r^{2} = π \cdot {(csc (\frac{π}{8}))}^{2} \approx 21.45 sq.units$ $color(white)("XXX")"Area" = pir^2 = pi*(csc(pi/8))^2 ~~ 21.45 "sq.units"$

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