Using your Head is Permitted

February 2015 riddle

Qiyang Lu has sent in the following puzzler, which he says has been bugging him for many years now, and which he says he came up with as an extension to the triangle inequality. (Thanks!)

Prove or disprove:

In any quadrilateral ABCD, it is always true that the sum of the lengths of the quadrilateral's three longest edges is longer than the sum of the lengths of its two diagonals.

This month, more than usual, please make sure your solution is elegant.

List of solvers:

Dan Dima (1 February 05:19)
Radu-Alexandru Todor (4 February 08:36)
Lorenz Reichel (6 February 07:04)
Zhengpeng Wu (10 February 18:12)
Daniel Bitin (11 February 00:00)
Li Li (11 February 08:02)
Zhuo Wang (13 February 08:10)
Zilin Jiang (16 February 01:00)
Yuping Luo (27 February 07:44)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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