Angle Subtended by an Arc of a Circle

A circle is divided into $5$ sectors with area equal to $1:2:3:4:5$. Find the angle subtended at the center of the circle by the largest sector.

In the given figure, $\mathrm{O}$ is the centre of the circle and $BA=AC$. If $\angle ABC=50°$, find $\angle BOC$ and $\angle BDC$.

In the figure, if $O$ is the centre of the circle, $\angle AOB$ is:

In figure, $\mathrm{PQ}$ is the diameter of the circle with centre $\mathrm{O}$. If $\angle \mathrm{PQR}=65°, \angle \mathrm{RPS}=40°$ & $\angle \mathrm{PQM}=50°$, find $\angle \mathrm{QPR}, \angle \mathrm{PRS} \& \angle \mathrm{QPM}$.

In the given figure, O is the centre of the circle, find the value of x

In the given figure, $O$ is the centre of the circle. Find the value of $x$.

In the given figure, $AB$ and $BC$ are two chords of a circle whose centre is $O$ such that $\angle ABO=\angle CBO$. If $AB=6 \mathrm{cm}$ and $\angle ABO=30°$, find the measures of $BC$ and $\angle AOC$.

In the circle, seg $AB$ is a diameter. Point $C$ is in the interior of the circle. Prove that $\angle ACB$ is an obtuse angle.

In the figure, if $\angle ABC=50°$ and $\angle BDC=40°$, calculate $\angle CDA$.

In the given figure, $O$ is centre and $\angle ABO=30°$, then $\angle ACB$ is

Find the angle $y$ from the diagram.

$A, B$and $C$ are three points on the circle with centre $O$ such that $\angle AOB=90°$ and $\angle AOC=110°$. Find $\angle BAC$.

$O$ is the centre of the circle. If $\angle OAB=40°$ and $\angle OCB=30°$, find $\angle AOC$

Two circles intersect at two points $A$ and $B$. $AD$ and $AC$ are diameters to the two circles (see Fig. 10.34). Prove that $B$ lies on the line segment $DC$.

Meerut is $64 \mathrm{km}$ from Delhi. Find the angle (in degrees) subtended at the centre of the earth by the arc joining these two towns. The Earth is regarded as a sphere of $6336 \mathrm{km}$radius​.

In the figure given below, $AOB$ is a diameter of the circle and $\angle AOC=110°$, find $\angle BDC$.

In the given figure $\text{'}O\text{'}$ is the center of the circle. $\angle AEB =130 °$ and $\angle EBC =20 °$, then find the value of $\angle BDA=$_____$°$.

The length of a chord of a circle is equal to its radius. If the measure of angle is $\text{'}k\text{'}$, subtended by this chord on the major segment, then find the value of $\text{'}k\text{'}?$

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of semicircle $\mathrm{ACB}$_____$°$.

$\mathrm{O}$is the centre of the circle. $\mathrm{AOB}$ is a diameter. $\angle \mathrm{COB}=40°$, then the degree measure of minor arc $\mathrm{AC}$ _____$°$.