$A$ circular pond has a diameter of $17.5 \, m$. It is surrounded by a $2 \, m$ wide path. Find the cost of constructing the path at the rate of $Rs. \, 25$ per $m^2$ (in $Rs.$).

In $\odot(O, r)$,$\overline{OA}$ and $\overline{OB}$ are two radii perpendicular to each other. If the perimeter of the minor sector formed by these radii is $20\,cm$,then $r = \ldots\,cm$.

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \, cm$ and $7 \, cm$ is (in $cm$):

In a circle with radius $21 \, cm$,the length of a minor arc is $33 \, cm$. Find the measure of the angle subtended at the centre by this arc. Also,find the area of the minor sector and the area of the minor segment formed by it.

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 $\pi$)

The maximum area of $\Delta ABC$ inscribed in a semicircle with radius $10 \, cm$ is ....... $cm^2$.