The line segment joining two points on a circle is called .

‘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

A semi - circle of diameter $1$ unit sits at the top of a semi-circle of diameter $2$ units. The shaded region inside the smaller semi-circle but outside the larger semi-circle is called a lune . The area of the lune 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 $PA$?

Let $AB$ be a sector of a circle with centre $O$ and radius $d.\angle AOB=\theta \left(<\frac{\pi }{2}\right)$ and $D$ be a point on $OA$ such that $BD$ is perpendicular$OA$. Let $E$ be the mid-point of $BD$ and $F$ be a point on the arc $AB$ such that $EF$ is parallel to $OA$. Then, the ratio of length of the arc$AF$ to the length of the arc $AB$ 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 $r=\frac{a+b+c}{2}$.