The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

Will it be true to say that the perimeter of a square circumscribing a circle of radius $a \, cm$ is $8 a \, cm$? Give reasons for your answer.

As shown in the diagram,$\overline{AC}$ is a diameter of the circle with centre $O$. $\Delta ABC$ is inscribed in the circle. If $AC = 35 \, cm$,$AB = 21 \, cm$ and $BC = 28 \, cm$,find the area of the shaded region in $cm^2$.

$\widehat{ACB}$ 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 $\pi$)

Find the difference of the areas of two segments of a circle formed by a chord of length $5 \, cm$ subtending an angle of $90^{\circ}$ at the centre.

Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)