The breadth of a rectangular plot is $75 \%$ of its length. If the perimeter of the plot is $1050 \, m,$ what is its area (in $, m^2$)?

Two circles touch each other externally. The sum of their areas is $130 \pi \text{ cm}^2$ and the distance between their centres is $14 \text{ cm}$. The radius of the smaller circle is . . . . . . $\text{cm}$.

The tangents drawn at points $A$ and $B$ of a circle with centre $O$ meet at $P$. If $\angle AOB = 120^{\circ}$ and $AP = 6 \text{ cm}$,then what is the area of triangle $APB$ (in $\text{cm}^{2}$)?

If the circumference of a circle is equal to the perimeter of a square,what is the ratio of the area of the circle to the area of the square?

The area of a circle is $154 \, cm^{2}$. The length of an arc of the circle which subtends an angle of $45^{\circ}$ at the centre is......$cm$.

Find the diameter of a wheel that makes $113$ revolutions to go $2 \, km$ $26 \, decametres$. (in $m$)