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Proving a theorem (Posted on 2016-02-12) Difficulty: 3 of 5
If a straight line meets the sides BC, CA, and AB of a triangle ABC in the points D, E, and F respectively
then
(AE/EC)* (CD/DB)* (BF/FA) = 1.

Prove the above theorem.

BTW the converse is also true.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts Huh? Comment 1 of 1
I just noticed this problem from a few weeks ago, and  I was initially puzzled.  It is not possible for a straight line to cross all sides of a triangle at three distinct points.  A straight line can only cross 0 or 2 sides (unless a straight line goes through A or B or C, which I am ruling out, because that makes D or E or F the same as A or B or C and the formula fails due to division by zero).

The only way this problem makes sense is if we are talking about extending the sides.  In which case, 1 (or 3) of D, E, and F are outside triangle A, B, C.

Unfortunately, I do not have a proof, but at least I have a way to make the problem make sense.  

  Posted by Steve Herman on 2016-03-26 22:59:10
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