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Routh's Theorem

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In triangle $ABC$ , $D$ , $E$ and $F$ are points on sides $BC$ , $AC$ , and $AB$ , respectively. Let $r=\frac{AF}{AB}$ , $s=\frac{BD}{BC}$ , and $=\frac{CE}{CA}$ . Let $G$ be the intersection of $AD$ and $BC$ , $H$ be the intersection of $BE$ and $CF$ , and $I$ be the intersection of $CF$ and $AD$ . Then, Routh's Theorem states that

$[GHI]=\dfrac{(rst-1)^2}{(rs+r+1)(st+s+1)(tr+t+1)}[ABC]$

[Asy_image]

Proof

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Categories: Incomplete material | Stubs | Geometry | Theorems | Definition

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