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The Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the intersection 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 =*x*, =*y*, and =*z*, the signed area of the triangle formed by the cevians*A**D*,*B**E*, and*C**F*is the area of triangle*A**B**C*times
This theorem was given by Edward John Routh on page 82 of his

Source: Wikipedia

Download GGB file

*Treatise on Analytical Statics with Numerous Examples*in 1896.Source: Wikipedia

Download GGB file

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