Routh's theorem

The set of Routh, named after Edward Routh, is a mathematical theorem to the geometry of the triangle. He makes the following statement about the area of triangles (see chart):

ABC is a triangle with area (outer triangle in the graph). Furthermore, let F, D and E points on the sides [AB ], [ BC] and [ AC]. The partial ratios are:

Of I, G and H, the intersections AD and CF, AD and BE or BE, and CF are denoted.

Then for the area of triangle GHI (inner triangle in the graphic):

The set of Ceva can be regarded as a special case of the theorem of Routh. Cut in fact, transversals, and at one point, the area of ​​the triangle is equal to 0 It can be concluded, that the statement of the theorem of Ceva.