Routh's theorem
id:
routh-s-theorem-226-3565950
title:
Routh's theorem
text:
In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states that if in triangle A B C points D, E, and F lie on segments B C, C A, and A B, then writing C D B D = x, A E C E = y, and B F A F = z, the signed area of the triangle formed by the cevians A D, B E, and C F is
- S A B C 2, where S A B C is the area of the triangle A B C. This theorem was given by Edward John Routh on page
brand slug:
wiki
category slug:
encyclopedia
description:
Area ratio of one triangle and the triangle formed by the intersections of three cevians
original url:
https://en.wikipedia.org/wiki/Routh%27s_theorem
date created:
2006-04-05T17:40:44Z
date modified:
2024-09-14T19:06:00Z
main entity:
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image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/e/e0/Routh_theorem2.svg","width":357,"height":275}
fields total:
13
integrity:
16