# Constructing Tangents to a Circle

## with a Compass and Straight-Edge

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Using a compass and straight edge, we will be constructing a tangent to a circle. As the construction steps are given, they will be illustrated for you.

To start your construction, make two vertices, A and B, somewhere near the center of your paper.

Construct a circle using point A as center so that point B lies outside the circle. Name the circle c1.

Draw a line segment with end points A and B.

Now, find the midpoint of segment AB. Set your compass point on A and draw an arc through the B.

Using the same radius on your compass, perform the same construction using B as the arc center. Make sure that the two arcs cross. Mark the intersections of the arcs as vertices C and D.

Draw a segment using C and D as endpoints. Mark the point where AB and CD cross as E.

Using E as the center. Make a arc of radius AE that crosses c1 twice. Mark the intersections of the arc with c1 as F and G.

Draw a line through F and B and another through G and B. Label these lines as t1 and t2, your tangent lines to c1.

Congratulations! Your construction is now complete!

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