The maximum area of a triangle inscribed in a semicircle having radius $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

The circumference of a circular ground is $352\, m$. Find the area of the ground (in $m^2$).

In the adjoining diagram, $\overline{ AB }$ and $\overline{ CD }$ are diameters of $\odot( O , 7\, cm )$ perpendicular to each other. $A$ circle is drawn with diameter $\overline{ OD }$. Find the area of the shaded region. (in $cm^2$)

In $\odot(O, 6)$, $\widehat{ABC}$ is a major arc and $m \angle AOC = 60^{\circ}$. Then, the length of major $\widehat{ABC}$ is ........... (in $\pi$)

In $\odot(O, r)$,chord $\overline{AB}$ subtends a right angle at the centre. The area of the minor segment $\overline{AB} \cup \widehat{ACB}$ is $114 \, cm^2$ and the area of $\Delta OAB$ is $200 \, cm^2$. Then,the area of the minor sector $OACB$ is ......... $cm^2$.