EXERCISE

If $\mathrm{AB}, \mathrm{AC}, \mathrm{PQ}$ are tangents in the fig, given below, $\mathrm{AB}=5 \mathrm{cm}$ and the perimeter of $△\mathrm{APQ}=k \mathrm{cm}$, then find the value of $k$.

In the fig., $\mathrm{ABC}$ is a right triangle right-angled at $\mathrm{B}$ such that $\mathrm{BC}=6 \mathrm{cm}$ and $\mathrm{AB}=8 \mathrm{cm}$. If the radius of its incircle is $k \mathrm{cm}$, then find the value of $k$.

In the figure a circle touches all the four sides of a quadrilateral $ABCD$ with $\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=7 \mathrm{cm}$ and $\mathrm{CD}=4 \mathrm{cm}$. Find $AD$.

In the figure, there are two concentric circles with center $\mathrm{O}$ of radii $5 \mathrm{cm}$ and $3 \mathrm{cm}$. From an external Point $\mathrm{P}$, tangents $\mathrm{PA}$ and $\mathrm{PB}$ are drawn to these circles. If $\mathrm{AP}=12 \mathrm{cm}$. If the length of $\mathrm{BP}=k\sqrt{10} cm$, then find the value of $k$.

In the fig., $\mathrm{AB}$ is a chord of length $16 \mathrm{cm}$ of a circle of radius $10 \mathrm{cm}$. The tangents at $\mathrm{A}$ and $\mathrm{B}$ intersect at a point $\mathrm{P}$. Find the length of $\mathrm{PA}$.

Two concentric circles are of diameters $30 \mathrm{cm}$ and $18 \mathrm{cm}$. Find the length of the chord of the larger circle which touches the smaller circle.

In the figure, $AB$ is a diameter of a circle with centre $O$ and $AT$ is a tangent. If $\angle AOQ=58°$, find $\angle ATQ$.

In the figure, tangents $PQ$ and $PR$ are drawn from an external point $P$ to a circle with centre $O$ such that $\angle RPQ=30°$. A chord $RS$ is drawn parallel to the tangent $PQ$. Find $\angle RQS$.