Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.

In the figure, a circle is inscribed in a $△PQR$. If $PQ=10 \mathrm{cm}$, $QR= 8 \mathrm{cm}$and $PR=12 \mathrm{cm},$ find the lengths of $QM,RN$ and $PL.$

In the figure, common tangents $PQ$ and $RS$ to two circles intersect at $A$. Prove that $PQ=RS$.

In the figure given $PQR$ is a triangle, sides $PQ$ and $PR$ are extended to touch circle at $B, C$ and $A$ as shown in figure. Prove that $PB=\frac{1}{2}\times \left(\mathrm{Perimeter}of△PQR\right)$

A triangle $\mathrm{ABC}$ is drawn to circumscribe a circle of radius $3 \mathrm{cm}$ such that the segments $\mathrm{BD}$ and $\mathrm{DC}$ into which $\mathrm{BC}$ is divided by the point of contact $\mathrm{D}$ are of length $9 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively (See adjacent figure). Find the sides $\mathrm{AB}$ and $\mathrm{AC}$.

What sort of a quadrilateral is formed by the tangents at the ends of two perpendicular diameters of a circle?