Definition
A tangent (or tangent line) is a line that intersects a circle or curve at exactly one point (the point of tangency).
Why It Matters
Tangent lines represent the instantaneous direction of motion along a curve and are the visual representation of derivatives in calculus.
Core Concepts
- Tangent to a Circle: A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency.
- Tangent Segments: Tangent segments to a circle from the same external point are congruent.