### Theory:

Working rule to construct a tangent to a circle (Using Alternate Segment Theorem):
Given the radius of a circle, let us learn how to construct a tangent to the circle using its alternate segment theorem.
Example:
Draw a circle of radius $$4$$ $$cm$$. At a point $$L$$ on it, draw a tangent to the circle using the alternate segment.

Rough Sketch:

Construction:

Step $$1$$: With $$O$$ as the centre, draw a circle of radius $$4$$ $$cm$$.

Step $$2$$: Take a point $$L$$ on the circle. Through $$L$$, draw any chord $$LM$$.

Step $$3$$: Take two points $$M$$ and $$N$$ distinct from $$L$$ on the circle, so that $$L$$, $$M$$ and $$N$$ are in anti-clockwise direction. Join $$LN$$ and $$NM$$.

Step $$4$$: Through $$L$$ draw a tangent $$TT'$$ such that $$\angle TLM$$ $$=$$ $$\angle MNL$$.

Step $$5$$: $$TT'$$ is the required tangent.