Routh's Theorem
Routh's Theorem
Suppose that in a triangle lines are drawn from the vertices to the opposite sides at points , , and . Let , , and denote the ratios , , and . Let the triangle formed inside be .
ABC
U
V
W
λ
μ
ν
AV
VC
CU
UB
BW
WA
ABC
RST
Routh's theorem states that .
area[RST]=area[ABC]
2
(λμν-1)
((μν+μ+1)(νλ+ν+1)(λμ+λ+1))