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 $\mathrm{CD}$.

In Figure $\mathrm{O} \text{and} {\mathrm{O}}^{\text{'}}$ are the centres of two intersecting circles and $\mathrm{APB}$ Is parallel to ${\mathrm{OO}}^{\text{'}}$. Prove that $\mathrm{AB}=2{\mathrm{OO}}^{\text{'}}$.

Two equal chords $AB$ and $CD$ of a circle intersect at $P,$show that $\mathrm{AP}=\mathrm{PD} \mathrm{and} \mathrm{BP}=\mathrm{CP}$.

In the given figure shows circle with Centre $O$, with equal chords $\mathrm{AB}$ and $\mathrm{CD};$ $\mathrm{OE}\perp \mathrm{CD}$ at $\mathrm{H}$ and $\mathrm{OF}\perp \mathrm{AB}$ at $\mathrm{G}$. Prove that $\mathrm{EH}=\mathrm{GF}$.