The degree measure of circle be${180}^{\circ }.$

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle ABD$ in degrees.

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle ABC$.

In the figure given below, $O$ is the centre of the circle and $AB$ is a diameter. If $AC=BD$ and $\angle AOC=72°$. Find $\angle BAD$.

A circular sheet of paper is divided into two sectors. The central angle of one of them is $160°$. These sectors are bent into cones of maximum volume. If the radius of the small cone is $8 \mathrm{cm}$, what is the radius of the other in $\mathrm{cm}$?

In the given figure $TP$ and $TQ$ are two tangents to the circle with centre $O$, touching at $A$ and $C$ respectively. If $\angle BCQ=55°$ and $\angle BAP=60°$, find$\angle AOC.$

In the figure given below $O$ is the centre of the circle. If the $QR=OP$ and angle $\angle ORP=20°$. Find the value of $x$ giving reasons.

In a circle of radius $21 \mathrm{cm}$, an arc subtends an angle of $60°$ at the centre. Find the length of the arc.

Let $AB$ be a sector of a circle with centre $O$ and radius $d.\angle AOB=\theta \left(<\frac{\pi }{2}\right)$ and $D$ be a point on $OA$ such that $BD$ is perpendicular$OA$. Let $E$ be the mid-point of $BD$ and $F$ be a point on the arc $AB$ such that $EF$ is parallel to $OA$. Then, the ratio of length of the arc$AF$ to the length of the arc $AB$ is

In the given figure $O$ is the centre of the circle, $\angle AOC=80°$

What is the measure of $\angle ABC$

In a circle of radius $21$cm an arc subtends an angle of $60°$ at the centre. Find the length of the arc.

In the given figure, $ABCDE$ is a pentagon inscribed in a circle such that $AC$ is a diameter and side $BC\parallel AE$. If $\angle BAC=50°$, find giving reason

$\angle BEC$