In given figure, PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle POQ$

A sector of radius $12 centimetres$ and central angle $120°$ is rolled up into a cone. What is the central angle of the sector to be used to make a cone of base radius $\sqrt{2} centimetres$ and height $4 centimetres$?

The length of two chords $AB$ and $CD$ of a circle of centre $O$ are equal and $\angle AOB=60°$ then, $\angle COD$ is

Only one circle can be drawn through three non collinear points.

In the given figure, $BC$ is the diameter of a circle and $\angle BAO=60°$ then $\angle ADC$ is equal to

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 $\angle EDC$.

Prove that, the angle in the semicircle is right angle.

$AB$ is the diameter of the circle. $D$ is the point on the circle.

$\angle ACB+\angle ADB+\angle AEB=270°$. The measure of one among $\angle ACB, \angle ADB$ and $\angle AEB$ is $110°$ . Write the measures of $\angle ACB, \angle ADB, \angle AEB$.

The angle subtended by the diameter of a circle at a point on the circumference is _____.

In the given figure $O$ is centre of a circle, $\angle AOB = 40°$ and $\angle BDC = 100°$ then the value of $\angle OBC$ will be

On the circle with center $O$, points $A,B$ are such that $OA = AB$. A point $C$ is located on the tangent at $B$ to the circle such that $A$ and $C$ are on the opposite sides of the line $OB$ and $AB=BC$. The line segment $AC$ intersects the circle again at $F$. Then the ratio $\angle BOF:\angle BOC$ is equal to -

In figure if $\angle OAB=40°$, then $\angle ACB$ is equal to

In the figure, the chord $\mathrm{BD}$ is perpendicular to the diameter $\mathrm{AC}$. Find the measure of $\angle CDM$. (in $°$).

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 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, $\mathrm{O}$ is the centre of a circle, $\mathrm{AC}$ is a diameter. If $\angle \mathrm{ACB} = 50°$, then find the measure of $\angle \mathrm{BAC}$(in $°$).