This shows how to construct the tangent to a circle at a given point on the circle with compass and straightedge or ruler. It works by using the fact that a tangent to a circle is perpendicular to the radius at the point of contact. It first creates a radius of the circle, then constructs a perpendicular to the radius at the given point.
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
The image below is the final drawing above.
|1||Line segment OR is a radius of the circle O.||It is a line from the center to the given point P on the circle.|
|2||SP is perpendicular to OR||By construction, SP is the perpendicular to OR at P. See Constructing a perpendicular to a line at a point for method and proof.|
|3||SP is the tangent to O at the point P||The tangent line is at right angles to the radius at the point of contact. See Tangent line definition.|