proof of Menelaus’ theorem
First we note that there are two different cases: Either the line connecting , and intersects two sides of the triangle or none of them. So in the first case that it intersects two of the triangle’s sides we get the following picture:
From this we follow (, and being undircted):
Mulitplying all this we get:
The second case is that the line connecting , and does not intersect any of the triangle’s sides:
In this case we get:
So multiplication again yields Menelaus’ theorem
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