This is the stepbystep, printable version. If you PRINT this page, any ads will not be printed.
See also the animated version.
After doing this  Your work should look like this 

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. 