Difference between revisions of "The Devil's Triangle"
Redfiretruck (talk | contribs) (→Proof 2) |
Redfiretruck (talk | contribs) (→Proof 2) |
||
Line 25: | Line 25: | ||
~@CoolJupiter | ~@CoolJupiter | ||
− | |||
− | |||
− | |||
− | |||
− | |||
=Other Remarks= | =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: | 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: |
Revision as of 10:14, 6 November 2020
Contents
[hide]Definition
For any triangle , let and be points on and respectively. Devil's Triangle Theorem states that if and , then .
Proofs
Proof 1
Proof by CoolJupiter:
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 .
~@CoolJupiter
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 .
Testimonials
The Ooga Booga Tribe would be proud of you. Amazing theorem - RedFireTruck
This is Routh's theorem isn't it~ Ilovepizza2020