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 $cm^2$.

In a circle with radius $56 \, cm$,find the area of the minor sector,the major sector,and the minor segment corresponding to two radii perpendicular to each other.

In a circle with radius $6 \, cm$,the area of a sector corresponding to an arc of length $12 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

As shown in the diagram,$\overline{OA}$ and $\overline{OB}$ are two radii of $\odot(O, 35 \text{ cm})$ perpendicular to each other. If $OD = 12 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

The radius of a circular ground is $35 \, m$. Inside it,a $3.5 \, m$ broad road runs around its boundary. $A$ part of the road between two radii forming an angle of measure $72^{\circ}$ at the centre is to be repaired. Find the cost of repairing at the rate of ₹ $80 / m^{2}$. (in ₹)

In a circle with radius $42 \ cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the minor segment corresponding to this arc. (Use $\sqrt{3} = 1.73$)