If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

In the adjacent figure, $AB$ is a chord of circle with centre $O$. $CD$ is the diameter perpendicular to $AB$. Show that $AD=BD$.

In the figure, $\text{'}O\text{'}$ is the centre of the circle. $\angle AOB=100°$ and $\angle ADB=k°$ then the value of $k$ is

In the figure, $\angle BAD=40°$. If the measure of $\angle BCD=k°$. Find $k$.

In the figure, $O$ is the centre of the circle and $\angle POR=120°$. Find $\angle PQR$ and $\angle PSR$.

If a parallelogram is cyclic, then it is a rectangle. Justify.

In the figure, $\text{'}O\text{'}$ is the centre of the circle. $OM=3 \mathrm{cm}$ and $AB=8 \mathrm{cm}$. Find the radius of the circle in $\mathrm{cm}$.

In the figure, $O$ is the centre of the circle and $OM\mathit{,}\mathit{ }ON$ are the perpendiculars from the centre to the chords $PQ$ and $RS$. $OM=ON$ and $PQ=6 \mathrm{cm}$. Find the length of $RS$ in $\mathrm{cm}$.

$A$ is the centre of the circle and $ABCD$ is a square. If $BD=4 \mathrm{cm}$ then find the radius of the circle in $\mathrm{cm}$.