# Wooga Looga Theorem

The Wooga Looga Theorem states that the solution to this problem by franzliszt:

In points are on sides such that . Find the ratio of to .

is this solution by RedFireTruck:

WLOG let , , . Then and , , . Then . Therefore the answer is .

and that the solution to this problem by Matholic:

The figure below shows a triangle ABC which area is 72cm2. If AD: DB = BE: EC =CF: FA =1: 5, find the area of triangle DEF

is this solution by franzliszt:

We apply Barycentric Coordinates w.r.t. . Let . Then we find that . In the barycentric coordinate system, the area formula is where is a random triangle and is the reference triangle. Using this, we find that so .