In the given figure, $\mathrm{AB}$ is a diameter of a circle with centre $\mathrm{O}$ and $\mathrm{CP}$ is the tangent to the circle at the point $\mathrm{C}$. If  $\mathrm{AP} = 20 \mathrm{cm} \mathrm{and} \mathrm{CP} = \mathrm{l}0 \mathrm{cm}$, then find the radius of the circle (in $\mathrm{cm}$).

 

In the given figure, $\mathrm{AB}$ is a diameter of a circle with centre $\mathrm{O}$ and $\mathrm{CP}$ is the tangent to the circle at the point $\mathrm{C}$. If $\mathrm{CP}=15 \mathrm{cm}$ and $\mathrm{BP}=7.5 \mathrm{cm}$, then find the radius $\left(\mathrm{cm}\right)$ of the circle.

In the given figure, $\mathrm{ABC}$ is a triangle in which $\mathrm{AB} = \mathrm{AC}$. A circle through $\mathrm{B}$ touches $\mathrm{AC} \mathrm{at} \mathrm{D}$ and intersects $\mathrm{AB} \mathrm{at} \mathrm{P}$. If $\mathrm{D}$ is the mid-point of $\mathrm{AC}$, then show that  $4\mathrm{AP}=\mathrm{AB}$.

In the given figure, $\mathrm{O}$ is the centre of a circle. Find the value of $\mathrm{b}$.

In the given figure, $AB$ is the diameter of a circle with centre $O$ and $\angle BCD=130°$.

Find $\angle DAB$.

In the given figure, $AB$ is the diameter of a circle with centre $O$ and $\angle BCD = 130°$.

Find $\angle DBA$.

In the given figure, $O$ is the centre of the circle and $\angle DAE=70°$. Giving suitable reasons, find the measure of $\angle BCD$.

In the given figure, $O$ is the centre of the circle and $\angle DAE = 70°$. Giving suitable reasons, find the measure of $\angle BOD$.

In the given figure, $O$ is the centre of the circle and $\angle DAE = 70°$. Giving suitable reasons, find the measure of $\angle OBD$.