How to construct (draw) a tangent to a circle

Tangent to a circle

Geometry construction using a compass and straightedge

- Printable problem worksheet
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Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

After doing this	Your work should look like this
We start with a point P somewhere on a given circle, with center point O. If the center is not given, you can use: "Finding the center of a circle with compass and straightedge or ruler", or "Finding the center of a circle with any right-angled object".
1. Draw a straight line through the center O of the circle and the point P right across the circle. This is a diameter of the circle.
2. Mark a point Q anywhere. For best accuracy, avoid putting it too close to the diameter line.
3. Place the compass on the point Q just drawn, and set it's width to the point P.
4. Without changing the width, draw an arc across the diameter line, creating point R.
5. Without changing its width, draw another arc on the opposite side of Q.
6. Using the straightedge, draw a line through R and Q, extending it onwards so it crosses the arc just drawn. Mark this point S.
7. Using the straightedge, draw a line through P and S, extending it in both directions.
8. Done. The line just drawn is the tangent to the circle O through point P.

How it works

Recall that the tangent to a circle is perpendicular to the radius at the contact point. (See Tangent definition page). This construction uses that fact in reverse. By constructing a line at right angles to the diameter it must be the tangent line. The method used to construct the perpendicular is exactly the same as the one used in "Construct a perpendicular at the end of a ray".

Try it yourself

Click here for a printable tangents construction 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.

Constructions pages on this site

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Triangle Centers

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Non-Euclidean constructions