Tangents through an external point - construction
This demonstration shows how to construct the two possible tangents to a given circle through a given external point using only a compass and straight edge. See "Introduction to Constructions" We start with a given circle with center O and and a point P outside the circle. The result is two tangent lines that pass through P.

To construct a tangent at a point on the circle see Tangent to a circle - construction.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
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Step-by-step Instructions
Step 1 Draw a straight line between the center O of the given circle and the given point P.
Step 2 Find the midpoint of this line by constructing the line's perpendicular bisector. See Constructing the Perpendicular Bisector of a Line Segment.
Step 3 Place the compass on the midpoint just constructed, and set it's width so that it passes through the center O of the circle..
Step 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.
Step 5 Draw the two tangent lines from P through J and K.
Step 6 Done. The two lines just drawn are tangential to the given circle and pass through P.
Try it yourself
Click here for a printable tangents construction worksheet with some problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions