A pair of tangents can be constructed to a circle inclined at an angle of $170°$.

Draw a circle of radius $2.8\mathrm{cm}$ with centre $O$. Construct a tangent to the circle at a point $P$ of the circle.

Draw a pair of tangents to a circle of radius $4\mathrm{cm}$ which are inclined to each other at an angle of $60°$.

Draw a circle of radius $4\mathrm{cm}$. Construct a pair of tangents to it, the angle between which is $60°$.

Construct a pair of tangents $PQ$ and $PR$ to a circle of radius $4 \mathrm{cm}$ from a point $P$ outside the circle $8 \mathrm{cm}$ away from the centre. Measure $PQ$ and $PR$. 

Draw two tangents to a circle of radius $3.5\mathrm{cm}$ from a point $P$ at a distance of $6.2\mathrm{cm}$ from its centre.

Draw a circle of radius $3cm$. Take two points $P$ and $Q$ on one of its extended diameter each at a distance of $7cm$ from its centre. Draw tangents to the circle from these two points $P$ and $Q$.

Draw a line segment $AB$ of length $8\mathrm{cm}$. Taking $A$ as centre, draw a circle of radius $4\mathrm{cm}$ and taking $B$ as centre, draw another circle of radius $3\mathrm{cm}$. Construct tangents to each circle from the centre of the other circle.

Draw a right triangle $ABC$ in which $AB=6cm, BC=8cm \text{and} \angle B=90°$. Draw $BD$ perpendicular from $B$ on $AC$ and draw a circle passing through the points $B,C \text{and} D$. Construct tangents from $A$ to this circle.