Intersecting chords theorem

When two chords of a circle intersect, the products of the segments into which each is divided are equal. This fact, also known as the power of a point, has surprising applications.

Theorem — Intersecting chords

If two chords $AB$ and $CD$ of a circle intersect at a point $S$, then: $SA \cdot SB = SC \cdot SD$

A worked exercise applying this theorem is given among the chapter exercises.

Links

Topics: Euclidean circle
Concepts: Chord · Power of a point
Methods: Circle chords
Skills: Synthetic geometry