Constructing tangents through an external point

Tangents through an external point - construction

- 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

This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.

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.
1. Draw a straight line between the center O of the given circle and the given point P.
2. Find the midpoint of this line by constructing the line's perpendicular bisector. (See Constructing the Perpendicular Bisector of a Line Segment.
3. Place the compass on the midpoint just constructed, and set it's width to the center O of the circle.
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.
5. Draw the two tangent lines from P through J and K.
6. Done. The two lines just drawn are tangential to the given circle and pass through P.

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.

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