In the given figure, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $\mathrm{AB}=24 \mathrm{cm}, \mathrm{OM}=5 \mathrm{cm}, \mathrm{ON}=12 \mathrm{cm}$. Find the radius of the circle.

In the given figure, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $\mathrm{AB}=24 \mathrm{cm}, \mathrm{OM}=5 \mathrm{cm}, \mathrm{ON}=12 \mathrm{cm}$. Find the length of chord $CD$.

In the given circle, $O$ is the centre. Chords $AD=CD$, if $\angle ABC=40°$, find $\angle ABD, \angle BOC$ and $\angle COD$.

In the quadrilateral $ABCD$, $AB=CD$ and $\angle CAD=35°$. Find $\angle ACB$ and prove that $ABCD$ is an isosceles trapezium.

In the circle with centre $O$, $PQ=QR=RS$ and $\angle QOS=116°$. Calculate $\angle POQ, \angle OQR, \angle OQS$ and $\angle SQR$.

In the circle with centre $O$, $\angle BOD=160°$, chord $BC=$chord $CD$. Find $\angle BOC, \angle OBD, \angle OBC$ and $\angle CBD$.

$AB$ is a side of a regular hexagon and $BC$ is a side of a regular nonagon. Find $\angle BOC, \angle AOB, \angle OBC, \angle OAC$ and $\angle ABC$.

In the given figure, $A, B, C$ are three points on the circumference of a circle with centre $O$. $\mathrm{arc} \mathrm{AB}=2 \mathrm{arc} \mathrm{BC}$ and $\angle AOB=108°$. Calculate: (i) $\angle BOC,$(ii) $\angle OAB,$ (iii) $\angle OAC$, (iv) $\angle BAC$

In the circle,$O$ is the centre, chords $AE=AD=DC$ and $\angle ABC=56°$. Find: $\angle CBD,$$\angle CBE,$$\angle BOC$,$\angle COD$