Chapter 34: Constructing A Tangent Line: Situation 28 From the MACMTL–CPTM Situations Project
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Published:2015
Pawel Nazarewicz, Sharon K. O'Kelley, Erik Jacobson, Glendon Blume, M. Kathleen Heid, Svetlana Konnova, 2015. "Constructing A Tangent Line: Situation 28 From the MACMTL–CPTM Situations Project", Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations, M. Kathleen Heid, Patricia S. Wilson, Glendon W. Blume
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A student in a Geometry class was given the following steps describing how to construct a tangent to a circle O from a point A exterior to the circle (see Figure 34.1).
After seeing this, the student asked how one knows that this is in fact the tangent line, or how one knows that ∠OBA is a right angle.
The student's questions are asking why the chosen method of construction is valid. In addressing these questions, it is useful to review the definition of tangent line as well as why a line tangent to a circle is perpendicular to the radius at the point of tangency. The inscribed angle theorem and properties of isosceles triangles can be used to prove that the line of tangency and its corresponding radius form a right angle.
