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 $\angle BAD=$_____

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

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

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.

Let $ABCD$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $AE=BE=CE=DE$. Suppose $\angle DAB, \angle ABC, \angle BCD$ is an arithmetic progression. Then the median of the set $\left\{\angle DAB,\angle ABC,\angle BCD\right\}$ is :-

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 $\angle ACD+\angle BED=$_____$°$