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See also the animated version.
|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",
|1. Draw a straight line from the center O, through the given point P and on beyond P.|
|In the following steps 2 - 6 we are constructing the perpendicular to the line OP at a point P. This is the same procedure as described in Constructing a perpendicular at a point on a line.|
|2. Put the compasses' point on P and set it to any width less than the distance OP. Then, on the line just drawn, draw an arc on each side of P. This creates the points Q and R as shown.|
|3. Set the compasses on Q and set it to any width greater than the distance QP.|
|4. Without changing the compasses' width, draw an arc approximately in the position shown on one side of P.|
|5. Without changing the compasses' width, move the compasses to R and make another arc across the first, creating point S.|
|6. Draw a line through P and S.|
|7. Done. The line PS just drawn is the tangent to the circle O through point P.|