What is meant by the regular polygon?

In the given figure, three circles with centres $A, B, C$ respectively touch each other externally. If $AB=5cm, BC=7cm$ and $CA=6cm$, then the radius of the circle with centre $A$ is

From the figure of $\odot \left(O,r\right)$ match the following. The correct option is _____

Match

$\left(1\right) \overline{AC}\cup \stackrel{⏜}{ABC}$                 $\left(a\right)2r$

$\left(2\right)\overline{OA}$ length                      $\left(b\right)r$

$\left(3\right)\overline{AC}$ length                      $\left(c\right)\mathrm{\pi r}+2\mathrm{r}$

‘O’ is the centre of the circle. The area of the shaded region in the given figure is $126 c{m}^2 , \overline{PQ} = \overline{PR}$ then the diameter $QR$ is:

If the measure of each exterior angle of a regular polygon is ${\left(51\frac{3}{7}\right)}^{\circ }$, then the ratio of the number of its diagonal to the number of its side is:

In the figure, $a, b, c$ are the sides of a right triangle where $c$ is the hypotenuse. Prove that the radius $r$ of the circle which touches the sides of the triangle is given by $r=\frac{a+b+c}{2}$.

All congruent polygon are _____.

The circumference of the base of a cylindrical vessel is $132 cm$ and its height is $25 cm$. Find the radius of the cylinder.

In the figure,$ABCDEF$ is a regular hexagon. Prove that $△BDF,$ drawn by joining alternate vertices is equilateral.

In the figure, $ABCDEF$ is a regular hexagon. Prove that $ACDF$ is a rectangle.