The Devil's Triangle
Revision as of 09:36, 6 November 2020 by Cooljupiter (talk | contribs) (Created page with "=Definition= For any triangle <math>\triangle ABC</math>, let <math>D, E</math> and <math>F</math> be points on <math>BC, AC</math> and <math>AB</math> respectively. Devil's T...")
Contents
[hide]Definition
For any triangle , let and be points on and respectively. Devil's Triangle Theorem states that if and , then .
Proof
Proof 1
We have the following ratios: .
Now notice that . We attempt to find the area of each of the smaller triangles. Notice that using the ratios derived earlier. Similarly, and .
Thus, .
Finally, we have .
Other Remarks
This theorem is a generalization of the Wooga Looga Theorem, which @RedFireTruck claims to have "rediscovered". The link to the theorem can be found here: https://artofproblemsolving.com/wiki/index.php/Wooga_Looga_Theorem
Essentially, Wooga Looga is a special case of this, specifically when .