Angle Subtended by a Chord at a Point

In the given figure $\text{'}O\text{'}$ is the centre of the circle and $AB, CD$ are equal chords. If $\angle AOB=70°$. If $\angle OCD=k°$, then find the value of $k$.

The given figure shows a circle with centre $\mathrm{O}$. Also, $\mathrm{PQ}=\mathrm{QR}=\mathrm{RS}$ and $\angle \mathrm{POS}=150°$. If $\angle \mathrm{PQR}=k°$, then find the value of $k$.

$∆\mathrm{ABC}$ is an equilateral triangle and $\mathrm{D}, \mathrm{E}$ are two points on the circle. Find $\angle \mathrm{BEC}$ and $\angle \mathrm{BDC}$.

In the given figure $\text{'}O\text{'}$ is the centre of the circle and $AB, CD$ are equal chords. If $\angle AOB=70°$. Find the angles of the $\Delta OCD$.

In the figure, $\angle BAD=40°$. If the measure of $\angle BCD=k°$. Find $k$.

In the figure given below, $\mathrm{PQ}=\mathrm{RS}$ and  $\angle \mathrm{ORS}=48°$, find $\angle \mathrm{OPQ}$ and $\angle \mathrm{ROS}$,

In the figure given below, if $\mathrm{AB}=\mathrm{CD}$ and $\angle \mathrm{AOB}=90°$,find angle $\angle \mathrm{COD}$ (in degree).

$\mathrm{PT}$ is a tangent to the circle at $\mathrm{T}.$ If $\angle \mathrm{ABC} = 70°$ and $\angle \mathrm{ACB} = 50°,$ calculate $\angle \mathrm{BAT}$.

$\mathrm{PT}$ is a tangent to the circle at $\mathrm{T}.$ If $\angle \mathrm{ABC} = 70°$ and $\angle \mathrm{ACB} = 50°,$ calculate $\angle \mathrm{CBT}$.

In the given figure, $\Delta ABC$ and $\Delta DBC$ are inscribed in a circle such that $\angle BAC=60°$ and $\angle DBC=$$50°.$Then $\angle BCD$ equal to

Equal chords of a circle subtend equal angles at

In the following figure, $\mathrm{PQ}$ is the tangent to the circle at $\mathrm{A}, \mathrm{DB}$ is the diameter and $\mathrm{O}$ is the centre of the circle. If $\angle \mathrm{ADB}=30°$ and $\angle \mathrm{CBD}=60°,$ calculate $\angle \mathrm{CDB}.$

In the above figure, O is the centre of the circle. The value of x is _____ degrees.

Bisectors of vertex angles $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a triangle $\mathrm{ABC}$ intersect its circumcircle at the points $\mathrm{D}, \mathrm{E}$ and $\mathrm{F}$ respectively. Prove that angle $\mathrm{EDF}=90°-\frac{1}{2}\angle \mathrm{A}.$

In the given figure, $\mathrm{PQ}$ is a tangent to the circle at $\mathrm{A}. \mathrm{AB}$ and $\mathrm{AD}$ are bisectors of $\angle \mathrm{CAQ}$ and $\angle \mathrm{PAC}.$ If $\angle \mathrm{BAQ} = 30°,$ prove that $\mathrm{BD}$ is diameter of the circle.
 

is $\angle \mathrm{PQR}=100°$ in the following figure, where $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are points on a circle with center $\mathrm{O}$. $\angle \mathrm{OPR}$ find

Draw a circle of radius $3.0$ cm. Draw two chords of length $3$ cm. Measure the angles made by each chord at the centre. Are the values of both the angles equal?

is the center of the circle $\mathrm{O}$ in the figure. The radius $\mathrm{OD}$ is perpendicular to the diameter $\mathrm{AB}$. If $\mathrm{C}$ is a point on the circle, then find $\angle \mathrm{ABD}$ and $\angle \mathrm{BCD}$.

$\mathrm{O}$ is the center of the circle in the figure. Chord $\mathrm{AB}=$ Chord $\mathrm{CD}$ and $\angle \mathrm{AOB}=70°$ then the value of $\angle \mathrm{OCD}$ is:

The length of a chord of a circle is equal to its radius. Give the value of the angle made by the chord at the centre.