Angle Subtended by an Arc of a Circle

In the given figure $\text{'}O\text{'}$ is the centre of the circle and $AB, CD$ are equal chords. If $\angle AOB=70°$. Find the angles of the $\Delta OCD$.

Draw a circle with any radius and then draw two chords equidistant from the centre.

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

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 $\mathrm{cm}$.

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 $\mathrm{cm}$.

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

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

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

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