This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.

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. The midpoint may be inside or outside the circle, depending on the circle size and the location of the given point. (See Constructing the Perpendicular Bisector of a Line Segment.)
3.  Place the compass on the midpoint just constructed, and set it's 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.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy method)
• Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object