In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

In the figure,arcs have been drawn with radii $14 \, cm$ each and with centres $P$,$Q$,and $R$. Find the area of the shaded region (in $cm^{2}$).

Area of a sector of a circle of radius $36 \, cm$ is $54 \pi \, cm^{2}$. Find the length of the corresponding arc of the sector (in $cm$). (in $\pi$)

If the sum of the circumferences of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle of radius $R$,then

In a circle of radius $21\, cm$,an arc subtends an angle of $60^{\circ}$ at the centre. Find:
$(i)$ the length of the arc
$(ii)$ area of the sector formed by the arc
$(iii)$ area of the segment formed by the corresponding chord [Use $\pi = \frac{22}{7}$]

Find the circumference and the area of a circle with diameter $42 \, cm$.