In the given figure, $PA$ and $PB$ are two tangents drawn from an external point $P$ to a circle with centre $C$ and radius $4 \mathrm{cm}$. If $PA\perp PB$, then find the length of each tangent.

 

If $PA$ and $PB$ are two tangents to a circle with centre $O$ such that $\angle APB=80°$. Then find the value of $\angle AOP$.

In the given figure, $O$ is the centre of the circle. $AB$ is the tangent to the circle at the point $P$. If $\angle APQ=58°$, then the measure of $\angle PQB$is

In the given figure, $O$ is the centre of the circle. $AB$ is the tangent to the circle at the point $P$. If $\angle PAO=30°$ then $\angle CPB+\angle ACP$ is equal to

In the given figure, $PQ$ is a tangent to the circle with centre $O$. $A$ is the point of contact. If $\angle PAB=67°$ then measure of $\angle AQB$ is 

In the given figure, two circles touch each other at $C$ and $AB$ is a tangent to both the circles. The measure of $\angle ACB$ is

$O$ is the centre of a circle of radius $5 \mathrm{cm}$. At a distance of $13 \mathrm{cm}$ from $O$, a point $P$ is taken. From this point, two tangents $PQ$ and $PR$ are drawn to the circle. Then, the area of quadrilateral $PQOR$ is

In the given figure, $PQR$ is a tangent to the circle at $Q$, whose centre is $O$ and $AB$ is a chord parallel to $PR$ such that $\angle BQR=70°$. Then, $\angle AQB=$?

The length of the tangent from an external point $P$ to a circle of radius $5 \mathrm{cm}$ is $10 \mathrm{cm}$. The distance of the point from the centre of the circle is