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.