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Constructing the tangents to a circle from a point

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

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.

Geometry construction with compass and straightedge or ruler or ruler
1.  Draw a straight line between the center O of the given circle and the given point P. Geometry construction with compass and straightedge or ruler or ruler

2.  Find the midpoint of this line by constructing the line's perpendicular bisector.

(See Constructing the Perpendicular Bisector of a Line Segment.

Geometry construction with compass and straightedge or ruler or ruler
3.  Place the compasses on the midpoint just constructed, and set its width to the center O of the circle. Geometry construction with compass and straightedge or ruler or ruler
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. Geometry construction with compass and straightedge or ruler or ruler
5.  Draw the two tangent lines from P through J and K. Geometry construction with compass and straightedge or ruler or ruler
6.  Done. The two lines just drawn are tangential to the given circle and pass through P. Geometry construction with compass and straightedge or ruler or ruler
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Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions