In the figure below, $\mathrm{AE}$ is the diameter of the circle. $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are points on the circle. The measure of $\angle \mathrm{ABC} = {140}^{°}.$

What is the measure of $\angle \mathrm{CAE}$?

Using ruler and compass only, construct a $∆ABC$ such that $BC=5 \mathrm{cm}$ and $AB=6.5 \mathrm{cm}$ and $\angle ABC=120°$. Construct a cyclic quadrilateral $ABCD$, such that $D$ is equidistant from $AB$ and $BC$.

$\mathrm{PQRS}$ is a cyclic quadrilateral. Given $\angle \mathrm{QPS}=73°$, $\angle \mathrm{PQS}=55°$ and $\angle \mathrm{PSR}=82°$, calculate $\angle \mathrm{QRS}$.

$PQRS$ is a cyclic quadrilateral. Given $\angle QPS = 73°, \angle PQS = 55°$ and $\angle PSR=82°$ calculate $\angle RQS$.

In the figure, $ABCD$ is a cyclic quadrilateral. Also, $\angle A+\angle D=210°, \angle D+\angle C=250°$. What is $\angle A+\angle C$?

$O$ is the centre of a circle and $AB$ a diameter. $ABCD$ is a cyclic quadrilateral. $\angle ABC=65°$,  $\angle DAC=40°$ then the measure of $\angle BCD$ is 

In the given figure $O$ is the centre of the circle, $\angle AOC=80°$

What is the measure of $\angle ADC$?

Construct a cyclic quadrilateral $PQRS$ with $PQ=4 \mathrm{cm}, QR=6 \mathrm{cm}, PR=7.5 \mathrm{cm}, QS=7 \mathrm{cm}$.

In the figure, $ABCD$ is a cyclic quadrilateral. Also, $\angle A+\angle D=210°, \angle D+\angle C=250°$. Find the measures of $\angle A$ and $\angle C$.

If two sides of a cyclic quadrilateral are parallel, then prove that other sides are equal and its diagonals are also equal to each other.

In the figure, the chord $\mathrm{BD}$ is perpendicular to the diameter $\mathrm{AC}$. If the measure of $\angle BCD$ is $k°$ then find the value of $k$.

In the figure, if $\angle \mathrm{A}={100}^{\circ }$ then $\angle \mathrm{C}=$?