10. Construction of a tangent to a circle using alternate segment theorem

Draw a circle of radius \(4\) \(cm\). Then, 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.