ABCD is a square with one vertex at the center of the circle and two vertices on the circle. What is the length of the diagonal of the square if the area of the circle is 100 square cm?
$\dfrac{10}{\sqrt{\pi}}\sqrt{2}cm$
$\dfrac{20}{\sqrt{\pi}}\sqrt{2}cm$
$\dfrac{30}{\sqrt{\pi}}\sqrt{2}cm$
$\dfrac{40}{\sqrt{\pi}}\sqrt{2}cm$
Explanation:
Area of circle = $\pi R^{2}$
=100 sq. cm
$R^{2}=\dfrac{100}{\pi}$ Or, $R =\dfrac{10}{\sqrt{\pi}}cm$
From the figure, side of square, a = Radius of circle, $R = \dfrac{10}{\sqrt{\pi}}cm$
Diagonal of the square = $a{\sqrt{2}}$
$=\dfrac{10}{\sqrt{\pi}}\sqrt{2}cm$
