How to Find a Tangent Line to a Circle

A tangent line, which extends infinitely in two directions, by definition, touches a circle at a single point. For this to hold true, the tangent line must also be perpendicular to the radius of the circle at that point of intersection. These two facts make finding a tangent line a fairly easy task geometrically. Finding the equation for a tangent line to a circle is much more difficult and only useful in higher mathematics courses and some engineering applications.

Things You'll Need

• Paper and pencil
• Compass (for drawing circles)
• Protractor
• Ruler

Instructions

1. Draw a circle on a sheet of paper with the compass if it is not already given. If you use graph paper, the process will be much easier. Mark the center of the circle.

2. Mark the point where the tangent line will touch the circle and draw a radius line from the center of the circle to the point.

3. Align the origin of the protractor with the intersection point on the edge of the circle and the baseline, or 0-degree line, with the radius. Place a mark on the paper where the scale indicates 90 degrees.

4. Align a ruler or straightedge with the intersection point on the circle and the 90-degree mark. Draw the tangent line along this edge.