Tangent to a Circle From a Point

This Tangent to a Circle From a Point activity & project also includes:

Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about both to describe a situation. A great quickie problem to help remind learners that just because a property looks evident doesn't mean it can just be stated without proof.

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CCSS: Designed
Instructional Ideas

  • Use before and after teaching construction techniques as a motivator or reward
  • Use as a refresher problem on circle or tangent properties as part of a larger review
Classroom Considerations

  • Student task is not separated from teacher notes and solution key

  • Elegant solution pulls from both triangle and circle properties to reach conclusions
  • Good example of using mathematical rigor to defend and prove something that seems evident from a diagram

  • Though introduced as a construction problem, no actual construction is performed—just using definitions to describe what is shown in a diagram
  • The circles are named C and D, but only diagrammed by the centers O and M, making them hard to follow through the explanations
Common Core