teorema de Routh

Geometrical theorem of triangles

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 {\displaystyle ABC} points D {\displaystyle D} , E {\displaystyle E} , and F {\displaystyle F} lie on segments B C {\displaystyle BC} , C A {\displaystyle CA} , and A B {\displaystyle AB} , then writing C D B D = x {\displaystyle {\tfrac {CD}{BD}}=x} , A E C E = y {\displaystyle {\tfrac {AE}{CE}}=y} , and B F A F = z {\displaystyle {\tfrac {BF}{AF}}...