### Abstract

This entry provides a geometric proof of the intersecting chords theorem. The theorem states that when two chords intersect each other inside a circle, the products of their segments are equal. After a short review of existing proofs in the literature, I decided to use a proof approach that employs reasoning about lengths of line segments, the orthogonality of two lines and the Pythagoras Law. Hence, one can understand the formalized proof easily with the knowledge of a few general geometric facts that are commonly taught in high-school. This theorem is the 55th theorem of the Top 100 Theorems list.

### License

BSD License

### Topics

- Mathematics/Geometry

### Session Chord_Segments

- Chord_Segments

### Depends on

- Basic Geometric Properties of Triangles

### Auto-related entries

- Ptolemy’s Theorem
- Euler’s Partition Theorem

## Cite

×

Chord_Segments-AFP

    @article{Chord_Segments-AFP,
      author  = {Lukas Bulwahn},
      title   = {Intersecting Chords Theorem},
      journal = {Archive of Formal Proofs},
      month   = {October},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Chord_Segments.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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