Cyclic Properties of a Circle

If $O$ is the centre of the circle and $A$,$B$ and $C$ are points on its circumference and $\angle AOC={130}^{\circ }$, find $\angle ABC$?

In the given figure, $\mathrm{ABCD}$ is a cyclic quadrilateral in which $\mathrm{DC}$ is produced to $E$ and $\mathrm{CF}$ is drawn parallel to $\mathrm{AB}$ such that $\angle \mathrm{ADC} = 95º$and $\angle \mathrm{ECF} = 20º$. Then,$\angle \mathrm{BAD} =$ ?

In a cyclic quadrilateral $ABCD$, What is the measure of the smaller of the two, if $\angle B - \angle D$ $=$${60}^{°}$ ?

$\mathrm{ABCD}$ is a parallelogram. $\mathrm{A}$ circle through $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ intersects $\mathrm{CD}$ (produced) at $\mathrm{E}$. Which of the following is/are correct?

$1. \mathrm{AE}=\mathrm{AD}$
$2. \mathrm{CD}=\mathrm{DE}$

Select the correct answer using the code given below:

$\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB}$ is parallel to $\mathrm{DC}$. The vertices $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ and $\mathrm{D}$ pass through a circle. Which of the following are correct?

$1. \mathrm{AD}=\mathrm{BC}$
$2. \angle \mathrm{A}+\angle \mathrm{C}={180}^{\mathrm{o}}$
$3. \angle \mathrm{A}+\angle \mathrm{D}={180}^{\mathrm{o}}$

Select the correct answer using the code given below:

Explain cyclic quadrilateral.

In the figure, $AB$ is a diameter of a circle.

Find $\angle AED+\angle DCB$

If $\angle P=105°$ of a cyclic quadrilateral $PQRS$, then the value of $\angle R$ is:

ABCD is a cyclic quadrilateral in which $\angle \mathrm{A}=\mathrm{x}°, \angle \mathrm{B}=5\mathrm{y}°, \angle \mathrm{C}=2\mathrm{x}° \mathrm{and} \angle \mathrm{D}=\mathrm{y}°$. what is the value of $(3\mathrm{x}-\mathrm{y})?$

ABCD is acyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and sides AD and BC meet at F, when produced. If $\angle ADE=80° \text{and} \angle AED=50°$, then what is measure of $\angle AFB?$

In the figure, points $P,Q,R$ and $S$ lie on a circle. Then the values of $x$ and $y$ are respectively

$ABCD$ is a cyclic quadrilateral in which $AB = 14.4 \mathrm{cm}, BC = 12.8 \mathrm{cm}$ and $CD = 9.6 \mathrm{cm}$. If $AC$ bisects $BD$, then what is the length of $AD$?

In figure $PQ$, is a chord of a circle with centre $O$ and $PT$ is its tangent at $P$. if $\angle QPT=60°$, then $\angle PRQ$ is

The side $AB$ and $DC$ of a cyclic quadrilateral $ABCD$ are produced to meet at $E$ and sides $AD$ and $BC$ are produced to meet at $F$. If $\angle ADC = 78°$ and $\angle BEC = 52°$, then find the measure of $\angle AFB$.

AB and AC are two chords of a circle, BT is a tangent at B where T and Care on the same side of the chord AB. If $\angle ABT=70°$, then the value of$\angle ACB$ is?
 

ABCD is a cyclic trapezium and $AB\parallel CD$. If AB be the diameter of the circle and $\angle CAB=30°$, then the value of $\angle ADC$ is?

Match the following column.

	Column I	Column II
$1.$	PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If $\angle QPR=35°$, then the value of $\angle PSR$ is equal to	$\left(p\right) 55°$
$2.$	In the above figure, the value of $\angle PRQ$ is equal to	$\left(q\right) 125°$
$3.$	In the above figure, the value of $\angle PQR$ is equal to	$\left(r\right) 35°$
		$\left(s\right) 90°$

Codes:

As per diagram find radius of circle with O as centre.

If $\angle A0B=66°$ where O is centre of the circle in the figure. From the information in the diagram solve for x if $\angle DOC=52°$.

Find x, If $\angle ABF=\angle CBF$.