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 .
The Wooga Looga Theorem can be used to prove many problems and should be a part of any geometry textbook. ~ilp2020