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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".
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| 1. Draw a straight line from the center O, through the given point P and on beyond P. |
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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.
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| 2. Put the compass 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. |
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| 3. Set the compass on Q and set it to any width greater than the distance QP. |
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| 4. Without changing the compass width, draw an arc approximately in the position shown on one side of P. |
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| 5. Without changing the compass width,
move the compass to R and make another arc across the first, creating point S. |
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| 6. Draw a line through P and S. |
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| 7. Done. The line PS just drawn is the tangent to the circle O through point P. |
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