Secants of a Circle

A secant is a line that intersects a circle at exactly two points. It continues beyond the circle on both sides.

If a line cuts the circle at points \(A\) and \(B\), then it is a secant and the segment \(AB\) inside the circle is a chord.

It's important to understand how a secant differs from related terms.

When a secant passes through a circle, it forms two main parts:

• External segment: The part of the secant that lies outside the circle.
• Internal segment: The part of the secant inside the circle, which is the chord.

A secant helps create central angles by connecting the centre of the circle to the points where the secant intersects the circle.

This is used to study arcs and inscribed angles.

Since secants pass through two points on the circle, they naturally define arcs on the circle.

Imagine shining a laser beam through a transparent circular disc. If the beam enters at one point and exits at another, the laser path behaves like a secant — cutting the circle at two points.

Secants appear in many real-life situations:

• Light passing through a circular lens
• A straight road cutting across a round park
• A chord played on a guitar string (string segment forms the chord; extended line is the secant)
• Any straight object slicing through a circular object