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

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

In a circle with radius $10\,cm$,the area of a minor sector is $40\,cm^2$. Then,the length of the arc corresponding to that sector is $\ldots \ldots \ldots \ldots \,cm$.

The closed figure formed by an arc of a circle and the radii through its end points is called .........

$A$ circular park is surrounded by a road $21\, m$ wide. If the radius of the park is $105\, m$,find the area of the road in $m^2$.

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 $r = \ldots\,cm$.