Constructing a Line Tangent to a Circle with a Compass and Straightedge

In this video, I show how to use a compass and straightedge to construct a line that is tangent to a circle. Constructing a perpendicular line through a point on a line is the concept behind constructing tangent lines. Constructions can be tricky to remember, but the key is to narrow the construction down to one of the basic construction techniques (constructing perpendicular lines, copying angles, copying line segments).