$A$ circular wire of diameter $112 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio of $9:7$. The small side of the rectangle is......$cm$.

The sides of a triangle are in the ratio $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$ and its perimeter is $91\, cm$. The difference of the length of the longest side and that of the shortest side is

The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

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 circumference of a circle is $176\, m$. Then,its area is

$AB$ and $CD$ are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is $17 \, cm$. The lengths of $AB$ and $CD$ are $10 \, cm$ and $24 \, cm$ respectively. The radius (in $cm$) of the circle is