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Routh's Theorem

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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

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

[Asy_image]

Proof

This proof is incomplete. You can help us out by completing it.

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