A piece of wire $20 \,cm$ long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle. (in $cm$)
$\frac{90}{\pi}$
$\frac{160}{\pi}$
$\frac{20}{\pi}$
$\frac{60}{\pi}$
In $\odot( O , 7),$ the length of $\widehat{ ABC }$ is $14 .$ Then, $\ldots \ldots .$ holds good.
The circumference of a circle is $88 \,cm$. The length of each side of a square inscribed in that circle is $\ldots \ldots \ldots cm$.
The maximum area of a triangle inscribed in a semicircle having radius $10\,cm$ is $\ldots \ldots \ldots . . cm ^{2} .$
In a circle with radius $6.3\, cm$, an are subtends an angle of measure $150$ at the centre. Find the length of this arc and the area of the sector formed by this arc.
In $Fig.$ arcs have been drawn of radius $21\, cm$ each with vertices $A , B , C$ and $D$ of quadrilateral $A B C D$ as centres. Find the area of the shaded region. (in $cm ^{2}$)