Angle Properties of Circle

In the adjoining figure, $O$ is the centre of a circle. If the length of chord $PQ$ is equal to the radius of the circle, then $\angle PRQ$ is

In the following figure it is given that O is the centre of the circle and $\angle AOC=130°$. Find $\angle ABC$

In the following figure $AD\parallel BC$. If $\angle ACB=35°$ find the measurement of $\angle DBC$.

If $O$ is the centre of the circle, find the value of $x$ in the following

If $O$ is the centre of the circle, find the value of $x$ in the following

If $O$ is the centre of the circle, find the value of $x$ in the following

If $O$ is the centre of the circle, find the value of $x$ in the following

If $O$ is the centre of the circle, find the value of $x$ in the following

If $O$ is the centre of the circle, find the value of $x$ in the following

Using given information, find the value of $x$in the following case

Using given information, find the value of $x$in the following case

Using given information, find the value of $x$in the following case

Using given information below, find the value of $x$in the following case

Using given information, find the value of $x$in the following case

Using given information, find the value of $x$in the following case

In the figure given below, $\mathrm{AP}$ and $\mathrm{BP}$ are tangents to the circle with centre $\mathrm{O}$. Given $\angle \mathrm{APB}=60°,$ calculate $\angle ACB$.

In the figure given below, $\mathrm{O}$ is the centre of the circle. $\mathrm{AB}$ is a diameter, $\mathrm{TPT}\text{'}$ is a tangent to the circle at $\mathrm{P}$. If $\angle \mathrm{BPT}\text{'}=30°$, calculate $\angle BOP$ .

In the figure given below, $O$ is the centre of the circle. The tangents at $B$ and $D$ meet at $P$. If $AB$ is parallel to $CD$ and $\angle ABC=55°$, find: $\angle BOD$ and $\angle BPD$.

In the figure given below, $BD$ bisects $\angle ABC$. Prove that $\frac{AB}{BD}=\frac{BE}{BC}$.

In the figure given below, $CP$ bisects $\angle ACB.$Prove that $DP$ bisects $\angle ADB$.