Math Open Reference
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 |
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We start with a given circle with center O, and a point P outside the circle. |
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| 1. Draw a straight line between the center O of the given circle and the given point P. |  |
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2. Find the midpoint of this line by constructing the line's perpendicular bisector. (See Constructing the Perpendicular Bisector of a Line Segment. |
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| 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. |  |