Triangle geometry problem

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Joined: Tue May 27, 2014 2:13 am UTC

Triangle geometry problem

Postby Lttlefoot » Tue May 27, 2014 2:20 am UTC

This is not a homework problem. I heard it many years ago and never really solved it - I've confirmed the answer is 50 by entering a bunch of trig on my calculator but don't know how to do it geometrically. Apologies if this has been explained before or if it's hard to read this description because this forum says I can't post images.

Basically the picture to draw is a large isosceles triangle with the bottom side horizontal. The angle at the top is 20 degrees (call it A) and the two base angles are 80 degrees (call them B and C)

Now draw a line from B that goes 60 degrees up from the horizontal until it meets the line AC at a point D.

Now draw a line from C that goes 50 degrees up from the horizontal until it meets the line AB at a point E (it will cross the line you just drew).

The question is to prove that angle AED equals 50 degrees.

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Re: Triangle geometry problem

Postby Tirian » Tue May 27, 2014 5:58 am UTC

I'm sure it's been discussed around here somewhere. You can Google for "world's hardest easy geometry problem". Personally, I disagree with the originator of the problem who gives two clues but doesn't tell you which supplementary lines to draw to make the problem possible. To me, the problem is still very challenging even if you knew which lines to draw, but that's just my experience.

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Re: Triangle geometry problem

Postby skullturf » Mon Jun 02, 2014 6:51 pm UTC

It's also sometimes called the "adventitious angles" problem, and Googling those words gives you some results.

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