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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

between points A and D

please construct a line (passing through point P),and

divide ABCD into two parts with equal area

- Thread starter Albert
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- Thread starter
- #1

- Jan 25, 2013

- 1,225

between points A and D

please construct a line (passing through point P),and

divide ABCD into two parts with equal area

- Jan 30, 2012

- 2,492

Do you know how Russian revolutionaries in the beginning of the 20th century wrote letters to their comrades from tsarist prisons? They would use milk to write hidden messages between the lines. (Yes, apparently, at that time, they served milk in prisons.) When milk was dry, it was invisible, but by holding the letter over a candle, the hidden message could be revealed. I have a feeling that something is written between the lines in this problem statement as well.

Is it not the line that passes through P and the centroid? As Wikipedia helpfully reminds, the centroid can be found by constructing the centroid of triangles into which the quadrilateral is divided by diagonals.

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- #3

- Feb 7, 2012

- 2,703

This strikes me as an extension of the pentagon problem.

I would include a diagram if I had time, but I expect Albert can provide one.

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- #4

- Jan 25, 2013

- 1,225

yes the construction of the diagram is similar to the pentagon problemThis strikes me as an extension of the pentagon problem.

I would include a diagram if I had time, but I expect Albert can provide one.

now ! here is the diagram