Intersecting chords theorem
id:
intersecting-chords-theorem-206-14600839
title:
Intersecting chords theorem
text:
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. More precisely, for two chords AC and BD intersecting in a point S the following equation holds: | A S | ⋅ | S C | = | B S | ⋅ | S D | The converse is true
brand slug:
wiki
category slug:
encyclopedia
description:
Geometry theorem relating the line segments created by intersecting chords in a circle
original url:
https://en.wikipedia.org/wiki/Intersecting_chords_theorem
date created:
2008-09-17T15:53:06Z
date modified:
2024-09-11T04:34:33Z
main entity:
{"identifier":"Q2266397","url":"https://www.wikidata.org/entity/Q2266397"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/5/5f/Chord_theorem.svg","width":362,"height":364}
fields total:
13
integrity:
16