Prove that "An exterior angle of cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle."

In the below figure, $\mathrm{ABCD}$ is a cyclic quadrilateral, find the angle opposite to $\angle A$.

$\mathrm{ABCD}$ is a cyclic quadrilateral in the figure. Find an angle opposite to $\angle \mathrm{B}$.

In the given figure, chord $\mathrm{MN}$ and chord $\mathrm{RS}$ intersect at point $\mathrm{D}$. If $\mathrm{RS}=18, \mathrm{MD}=9$, $\mathrm{DN}=8$, then find $\mathrm{DS}$.

A circle divides a plane into 3 parts – points outside the circle, points inside the circle and points on the circle.

Name the points that are concyclic.

In figure $\mathrm{m}(arc \mathrm{WY})=44°$, $\mathrm{m}(arc\mathrm{ZX})=68°$, then if $\mathrm{WT}=4.8, \mathrm{TX}=8.0,$ $\mathrm{YT}=6.4$, find $\mathrm{TZ}$.

If $A, B, C$ and $D$ are four points such that $\angle BAC=45°$ and $\angle BDC=45°,$ then $A,B,C,D$ are concyclic.

In figure $m(arc\mathrm{WY})=44°$, $\mathrm{m}(arc\mathrm{ZX})=68°$, then If $\mathrm{WX}=25, \mathrm{YT}=8$, $\mathrm{YZ}=26$ find $\mathrm{WT}$.

The points $\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E}$ and $\mathrm{F}$ are not concyclic points.

In the given figure, altitudes $\mathrm{YZ}$ and $\mathrm{XT}$ of $\mathrm{\Delta WXY}$ intersect at $\mathrm{P}$. Prove that, Points $\mathrm{X},\mathrm{Z},\mathrm{T},\mathrm{Y}$ are concyclic.

$\angle \mathrm{ABC}$ is opposite to $\angle \mathrm{D}$.

Draw a circle and inscribe the trapezium. If a polygon of the given type can't be inscribed, write not possible.

In the figure $7.49,$ two circles with centres $\mathrm{O}$ and $\mathrm{P}$ are touching internally at point $\mathrm{A}.$ If $\mathrm{BQ}=9,\mathrm{DE}=5,$ complete the following activity to find the radii of the circles.

If the diagonals of cyclic quadrilateral are equal, then the quadrilateral is