Geometry/Chapter 9/Lesson 2

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  • Properties of Tangents
  • Properties of Arcs and Chords

Properties of Tangents[edit]

  1. If a line is a tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

With this property, your teachers will usually throw Pythagorean triples at you for you to solve. Yes... these triples still matter. For example:


AB is tangent to C at [point] D. Find the length of a radius of C.

Remember: Tangent AB and a radius of C form a right triangle. Use the Pythagorean theorem with whatever inputs your teacher decides to use.

  1. If a line in the same plane as a circle is perpendicular to a radius at its endpoint on the circle, then the line is a tangent to the circle.
  2. Two segments tangent to a circle form a point outside the circle are congruent.