# geometry problem

• Aug 9th 2012, 09:15 AM
surjective
geometry problem
hey,

Help is needed with the following geometry problem:

Consider a triangle ABC. Insert a point D on the side Ac and a point E on the side AB. Draw a line through DE. The intersection between the line through DE and the line through BC is called F.

Drawing an arbitrary triangle as mentioned above we can compute the following:

|BF|*|AE|*|CD|

It is possible to draw the triangle in a program called geogebra. By doing this we can move the points D and E and observe the change.

The question is the following: formulate an expression which apparently holds true for the above-mentioned triangle.

Thanks a bunch.
• Aug 9th 2012, 09:21 AM
richard1234
Re: geometry problem
I think you are referring to Menelaus' theorem, in that case, the ratio |AD|*|CF|*|BE| to |BF|*|AE|*|CD| is 1, i.e. they're equal.
• Aug 9th 2012, 04:08 PM
surjective
Re: geometry problem
Thank you very much. Just one more question. I looked up the theorem on the Internet and sometimes I came across the ratio as being 1. why the differene?
• Aug 9th 2012, 10:03 PM
richard1234
Re: geometry problem
Some texts say 1 or -1, it's -1 if you treat them as vectors (e.g. AD = -DA). But if you're concerned only with magnitudes (e.g. |AD|), it's 1.