Theory:

Working rule to construct a tangent to a circle (Using the centre):
Given the radius of a circle, let us learn how to construct a tangent to the circle using its centre.
Example:
Draw a circle of radius \(3\) \(cm\). Take a point \(P\) on this circle and draw a tangent at \(P\).
 
Rough Sketch:
 
Const_R_1.png
 
Construction:
 
Step \(1\): Draw a circle with centre at \(O\) of radius \(3\) \(cm\).
 
Step \(2\): Take a point \(P\) on the circle and join \(OP\).
 
Step \(3\): Draw perpendicular line \(TT'\) to \(OP\) which passes through \(P\).

Step \(4\): \(TT'\) is the required tangent.
 
Cons_1_GIF.gif