The length of the common chord of two equal intersecting circles is $10 \mathrm{cm}$ and the distance between the two centres is $6 \mathrm{cm}$, if the radius of each circle is $k.83 cm$ then find the value of $k$.

In the figure, $\mathrm{AB}=8 \mathrm{cm}, \mathrm{CM}=1 \mathrm{cm}$, $\mathrm{CM}$ is the perpendicular bisector of $\mathrm{AB},$ radius $\mathrm{OA}=x\mathit{ }\mathrm{cm}$. Find $x$.

In the given Figure, $\mathrm{CD}$ is the perpendicular bisector of the chord $\mathrm{AB}.$If, $\mathrm{AB}=2 \mathrm{cm} \mathrm{and} \mathrm{CD}=4 \mathrm{cm}$, if the radius of the circle is $k cm$ then find the value of $k$ in decimal.

In the given Figure $\mathrm{OD}$ is perpendicular to the chord $AB$ of a circle whose centre is $O$. Prove that $\mathrm{CA}=2\mathrm{OD}$.

In Figure $\mathrm{OMNP}$ is a square. A circle drawn with centre $O$ cuts the square in $X$ and $Y$. Prove that: $∆\mathrm{OXM}\cong ∆\mathrm{OYP}$, Hence prove that $\mathrm{NX}=\mathrm{NY}$.

Find the centre of a given circle.

Drawn an arc of a circle to pass through three points $A,B$ and $C$ not in the same straight line.

Two chords $\mathrm{AB}$ and $\mathrm{CD}$ of a circle are parallel and a line $L$ is the perpendicular bisector of $\mathrm{AB}$. Show that $L$ bisects $\mathrm{CD}$.