The point of concurrence of all angle bisectors of a triangle is called the _____.

The circle which passes through all the vertices of a triangle is called the _____.

Length of a chord of a circle is $24 \mathrm{cm}$. If the distance of the chord from the centre is $5 \mathrm{cm}$, then the radius of that circle is _____.

The length of the longest chord of the circle with radius $2.9$$\text{ cm}$ is _____.

Radius of a circle with centre $O$ is $4$ $\text{cm}$. If $l\left(OP\right)$ = $4.2$$\text{ cm}$, say where point $P$ will lie.

The lengths of parallel chords which are on opposite sides of the centre of a circle are $6$$\text{ cm}$ and $8$$\text{ cm}$. If the radius of the circle is $5$$\text{ cm}$, then the distance between these chords is

Construct incircle and circumcircle of an equilateral $\Delta DSP$ with side $7.5$$\text{cm}$. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

Construct $\Delta NTS$ where $\mathrm{NT}=5.7 \mathrm{cm}$, $TS=7.5$cm and $\angle NTS=110°$ and draw incircle and circumcircle of it.

In the figure given below, $C$ is the centre of the circle, seg $QT$ is a diameter where $CT=13,CP=5$, if the length of chord $RS$ is $k$ units then find $k$.