The length of a diagonal of a square inscribed in a circle with radius $10\, cm$ is $\ldots \ldots \ldots . cm$.

An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio $1: 2: 3$,then find the ratio of the areas of the three regions.

If the length of an arc of a circle of radius $r$ is equal to that of an arc of a circle of radius $2r$,then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

In a circle with radius $21 \ cm$,the perimeter of a minor sector is $64 \ cm$. Then,the length of the arc of that sector is $\ldots \ cm$.

In $\odot(O, 12)$, minor $\widehat{ACB}$ subtends an angle of measure $30^{\circ}$ at the centre. Then, the length of major $\widehat{ADB}$ is $\ldots \ldots \ldots \text{ cm}$. (in $\pi$)

$\widehat{ACB}$ is a minor arc of $\odot(O, 8 \, cm)$. If $m\angle AOB = 45^\circ$, the length of minor $\widehat{ACB}$ is $\dots \, cm$. (in $\pi$)