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#### Albert

##### Well-known member

- Jan 25, 2013

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through point A),and divide ABCDE into two parts with equal

area

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- Jan 25, 2013

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through point A),and divide ABCDE into two parts with equal

area

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- Jan 26, 2012

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- Jan 25, 2013

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A general pentagon(convex)Is this a general pentagon, or a particular pentagon?

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through point A),and divide ABCDE into two parts with equal

area

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- Jan 25, 2013

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In my opinion the best proof is "a proof without words"

so again I construct a diagram and let it explain the solution

and AG is what we need as written by Opalg

"if [FONT=MathJax_Math]*M*[/FONT] is the midpoint of [FONT=MathJax_Math]*P*[/FONT][FONT=MathJax_Math]*Q*[/FONT] then the line [FONT=MathJax_Math]*A*[/FONT][FONT=MathJax_Math]*M*[/FONT] will do the job"

so again I construct a diagram and let it explain the solution

and AG is what we need as written by Opalg

"if [FONT=MathJax_Math]

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- Jan 25, 2013

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The statement M lies between C and D is not always trueReferring to Albert's beautiful solution to the problem in his earlier thread, if $M$ is the midpoint of $PQ$ then the line $AM$ will do the job,provided that$M$ lies between $C$ and $D$. I imagine that this must necessarily be the case, but I don't see how to prove it.

in fact M and C (or M and D)may coincide

May M also lie between D and E ?(if the length of CD is very small)

M may also lie between B and C.

(we may check this using various diagram)

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