Constructing a Tangent to a Circle

using a straight edge and a compass

Step 1: Construct a circle with a radius of any size. Name the circle C1.

Step 2: Construct a point on the circle. Call it D.

Step 3: Construct a point off of the circle. Call it E. See sketch 1.

Step 4: Construct a line through point D and point E. Name the line m.

Step 5: Construct a line through the center of the circle and point E. Name the line n. See sketch 2.

Step 6: (Hide the lines.) Construct a line segment between point P and the center of the circle C1.

Step 7: Construct the midpoint of the segment. Name the midpoint J. See sketch 3.

Step 8: Construct a circle using the center and a point. The center will be at point J while the radius is the distance between point J and the center of the circle C1. (Select J first and then while holding the shift also select the center of the circle C1.) See sketch 4.

Step 9: Construct the intersection between the two circles. Name these points L and K. See sketch 5.

Step 10: (Hide the circle whose center is J and hide the line segment.) Construct a line through L and P. (For the other tangent, construct a line through K and P.) See sketch 6.

Finally, let's prove that these line are tangents to C1. Remember that the tangent line(s) is(are) perpendicular to radii. Construct a line segment between L and the center of the circle C1. Now measure angle L. See sketch 7. The measurement of a perpendicular angle is 90.

Click on the next window to see the actual construction of two tangents to a circle! Remeber to start with three points. The first point is the center of your circle. The second point is a point on the circle. The last point is a point outside your circle. (Hold the shift key while you are creating your points.) Start the script.