Tangents and Slopes

learning_notes

Last updated: 8/16/2025

Key Concepts:

  • Tangent Lines – A tangent line touches a circle at exactly one point and is perpendicular to the radius at that point.
  • Slope of Tangents – The negative reciprocal of the slope of the radius gives the slope of the tangent.
  • Two Tangents Theorem – If two tangents are drawn from a common point outside the circle, their lengths are equal.

Skills Covered:

  • Finding the slope and equation of a tangent at a certain point.
  • Using two tangents theorem to prove congruence or calculate length.

Example Problem:

  • A circle has center ((3, -2)) and a point ((7, -2)) on its circumference. Find the equation of the tangent line at this point.

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