Cyclic Quadrilateral and its Properties

$ABCD$is cyclic quadrilateral, lines $AB$and $DC$intersect in the point $F$ and lines $AD$and $BC$intersect in the point $E$. Show that the circumcircles of $ABCF$and $ACDE$intersect in a point $G$ on the line $EF$.

Difference between the measures of the opposite angles of a cyclic quadrilateral is $12°$. Find the meaures of both the angles.

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

In the diagram given below $ABCD$ is a cyclic quadrilateral. The value of $\angle BAD=$_____

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 $\angle ABF=\angle CBF$.

In the diagram given below $ABCD$ is a cyclic quadrilateral. Then $\angle BAD=\angle BCE$

In the diagram given below $ABCD$ is a cyclic quadrilateral. If the value of $\angle BCD=100°$, then the value of $\angle BCE=70°$.

In the diagram given below $ABCD$ is a cyclic quadrilateral. The value of $\angle BCE=$_____$°$

In the diagram given below $ABCD$ is a cyclic quadrilateral. The value of $\angle BCE=$

If a pair of opposite angles of a quadrilateral is complementary, then the quadrilateral is cyclic quadrilateral

If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is _____ quadrilateral

If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is 

What is converse of theorem on cyclic quadrilateral?

State and prove corollary on cyclic quadrilateral.

If O is the centre of the circle then what is the value of x.

In figure, $AOB$  is the diameter of a circle and $C,D \text{and} E$ are three points situated on semi circle. The value of $\angle ACD+\angle BED=$_____$°$

$\square ABCD$ is cyclic. If $\angle B=110°$, then find the measure of $\angle D$.

In the given figure, $\mathrm{C}$ and $\mathrm{D}$ are points on the semi-circle described on $\mathrm{AB}$ as diameter. Given that, angle $\mathrm{BAD} = 70°$ and angle $\mathrm{DBC} = 30°$, then calculate angle $\mathrm{BDC}.$

$\mathrm{ABCDE}$ is a cyclic pentagon with centre of its circumcircle at point $\mathrm{O}$ such that $\mathrm{AB}=\mathrm{BC}=\mathrm{CD}$ and angle $\mathrm{ABC}=120°$. Calculate $\angle \mathrm{BED}$.