David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735

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Two Lines Tangent to a Circle

Starting with a circle and a point outside the circle, our goal will be to construct two distinct lines that are tangent to the circle and pass through the given circle.

First, draw the inversion of the point across the circle. To do so select "Inversion" from the choice menu and follow the on screen instructions.

Next, draw a line connecting the point and it's inversion point that you just constructed. Now draw a line through the inversion point perpendicular to the line segment you just drew.

This line intersects the circle in two points. Mark these points of intersection. Now draw two lines, one for each intersection point just found, going through the original point. These two lines are tangent to the circle. Can you explain why?