Answer the following question by looking at the given figure: Name the three chords.

‘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:

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                      $\left(c\right)\mathrm{\pi r}+2\mathrm{r}$

Chords $AB$ and $CD$ are intersecting at $P$. $AB=10$ centimetres, $PB=4$ centimetres and $PD=3$ centimetres. What is the length of $PA$?

On the circle with center $O$, points $A,B$ are such that $OA = AB$. A point $C$ is located on the tangent at $B$ to the circle such that $A$ and $C$ are on the opposite sides of the line $OB$ and $AB=BC$. The line segment $AC$ intersects the circle again at $F$. Then the ratio $\angle BOF:\angle BOC$ is equal to -

The two chords $AB$ and $CD$ of a circle are at equal distance from the centre $O$. If $\angle AOB=60°$ and $CD=6 cm$, then calculate the length of the radius of the circle.

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 $r=\frac{a+b+c}{2}$.