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 $\mathrm{EH}=\mathrm{GF}$.

In Figure $C$ is the centre of the circle.$\mathrm{CB}$ bisects the $\angle \mathrm{DBE}$, $\mathrm{CD}\perp \mathrm{PQ}$ and $\mathrm{CE}\perp \mathrm{RS}$. Prove that $\mathrm{PQ}=\mathrm{RS}$.

In the given Figure, $AB$ and $CD$ Are equal chords of a circle whose Centre is $O.$ $\mathrm{OM}\perp \mathrm{AB}$ and $\mathrm{ON}\perp \mathrm{CD}$ prove that $\angle \mathrm{OMN}=\angle \mathrm{ONM}$.

If $m\stackrel{⏜}{QR}$ is $k°$, find the value of $k$.

Find: $m\angle BOC$