Intersecting chords theorem
Geometry theorem relating the line segments created by intersecting chords in a circle
Intersecting chords theorem
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements. For example, for two chords AC and BD intersecting at point S, the following equation holds: | A S | ⋅ | S C | = | B S | ⋅ | S D | {\displaystyle |AS|\cdot |SC|=|BS|\cdot |SD|}
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