# Difference between revisions of "Routh's Theorem"

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==Proof== | ==Proof== | ||

− | + | Scale [[triangle]]<math>ABC</math>'s area down so that it becomes 1. We can then use Menelaus's Theorem on [[triangle]] <math>ABD</math> and line <math>FHC</math>. | |

<math>\frac{AF}{FB}\times\frac{BC}{CD}\times\frac{DG}{GA}= 1</math> | <math>\frac{AF}{FB}\times\frac{BC}{CD}\times\frac{DG}{GA}= 1</math> | ||

This means <math>\frac{DG}{GA}= \frac{BF}{FA}\times\frac{DC}{CB} = \frac{rs}{s+1}</math> | This means <math>\frac{DG}{GA}= \frac{BF}{FA}\times\frac{DC}{CB} = \frac{rs}{s+1}</math> |

## Latest revision as of 23:02, 23 March 2021

In triangle , , and are points on sides , , and , respectively. Let , , and . Let be the intersection of and , be the intersection of and , and be the intersection of and . Then, **Routh's Theorem** states that

## Proof

Scale triangle's area down so that it becomes 1. We can then use Menelaus's Theorem on triangle and line . This means

Full proof: https://en.wikipedia.org/wiki/Routh%27s_theorem

## See also

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