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I need to prove the following statement and I would really need help visualizing it. If someone could provide me with a picture, it would be extremely helpful.

"If A,B,D,E,N,M are six points such that the lines AE,DM,NB are concurrent and AM,DB,NE are concurrent, what can be said about the lines AB,DE,NM?"

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Consider Pappus' theorem with the unusual notation given below:

enter image description here

Here, two straight lines, $a$ and $b$ are given. On $a$ there are some points $AE$, $DM$, and $NB$. On $b$ there are some other points $BD$, $EN$, and $AM$. Connect the points with the red, the yellow, and the blue lines called $D$, $E$, $B$, $A$, and $M$, $N$. (The letters used to denote the lines are the common letters of the notation of the points connected.) Then, $DE$ denotes the intersection of $D$ and $E$; $BA$ denotes the intersection of $B$ and $A$; and $MN$ denotes the intersection of $M$ and $N$. According to Pappus' theorem $DE$, $BA$, and $MN$ sit on a straight line called $c$.

Now, let's use the principle of duality and let $A$, $B$, $D$, $E$, $M$, $a$, $b$, and c, and $M$ denote points. Then, translate Pappus' theorem as shown below.

enter image description here

The result of the translation is exactly the OP's theorem, the dual of Pappus's theore to be proved.

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