### 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:

**: With \(O\) as the centre, draw a circle of radius \(4\) \(cm\).**

*Step \(1\)***: Take a point \(L\) on the circle. Through \(L\), draw any chord \(LM\).**

*Step \(2\)***: 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 \(3\)***: Through \(L\) draw a tangent \(TT'\) such that \(\angle TLM\) \(=\) \(\angle MNL\).**

*Step \(4\)***: \(TT'\) is the required tangent.**

*Step \(5\)*