We start with a given circle with center O, and a point P outside the circle.


1. Draw a straight line between the center O of the given circle and the given point P. 

2. Find the midpoint
of this line by constructing the line's perpendicular bisector.
(See
Constructing the Perpendicular Bisector of a Line Segment. 

3. Place the compasses on the midpoint just constructed,
and set its width to the center O of the circle. 

4. Without changing the width, draw an arc across the circle in the two possible places.
These are the contact points J, K for the tangents. 

5. Draw the two tangent
lines from P through J and K. 

6. Done. The two lines just drawn are tangential to the given circle and pass through P. 
