Andromeda
Note

Secants

Definition

A secant is a line that intersects a circle or curve at exactly two distinct points.

Why It Matters

Secant lines represent the average rate of change between two points on a curve. In calculus, the limit of the secant line’s slope as the points move closer together defines the tangent line’s slope.

Core Concepts

  • Secant Segment Theorem: If two secants are drawn to a circle from an external point, the product of the external secant segment and the entire secant segment is constant: APBP=CPDPAP \cdot BP = CP \cdot DP.
    • How to read: “A P times B P equals C P times D P.”
    • Meaning: The product of the outer segment and the entire secant is equal for both lines drawn from the same point.

Connected Concepts