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.
Printable step-by-step instructions
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.
Proof
The image below is the final drawing above.
Argument
Reason
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.
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.
-
Q.E.D
Try it yourself
Click here for a printable tangents problem 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 pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
Non-Euclidean constructions
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