Prove that $DD'$ also passes through $O$

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Question - if $C$,$D$ divide $AB$ harmonically and $C'$, $D'$ divide $A'B'$ harmonically and lines $AA'$, $BB'$, $CC'$ meet at $O$ ..prove that $DD'$ also passes through $O$...

My try - I have spent a sufficient amount of time in this question but not getting anywhere. I draw two straight lines one above the other... but not getting how to use Menelaus or Ceva... Any hint will be very helpful. Thanks

Source - CTPCM

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This is a property of harmonic pencils of lines for which one can define an attached cross ratio. See :

http://alexanderrem.weebly.com/uploads/7/2/5/6/72566533/projectivegeometry.pdf

http://users.math.uoc.gr/~pamfilos/eGallery/problems/Harmonic_Bundle.html