An interesting problem related to ratio

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MATHPRITOM
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An interesting problem related to ratio

Unread post by MATHPRITOM » Thu Feb 02, 2012 7:28 pm

Let, ABCD be a quadrilateral . P,Q,R,S are points on AB,BC,CD & DA such that BP:AP=BQ:CQ=DR:CR=DS:AS. PR & QS meets at O. Prove that, PO= RO.

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nafistiham
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Re: An interesting problem related to ratio

Unread post by nafistiham » Fri Feb 03, 2012 12:50 am

midpoints of sides of any quadrilateral make a parallellogram.do we need the information such that $BP:AP=BQ:CQ=DR:CR=DS:AS$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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MATHPRITOM
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Re: An interesting problem related to ratio

Unread post by MATHPRITOM » Sat Feb 04, 2012 7:51 pm

Here, P,Q,R,S ARE NOT MIDPOINTS. ANY PONT.

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Re: An interesting problem related to ratio

Unread post by nafistiham » Sun Feb 05, 2012 2:43 pm

nafistiham wrote:midpoints of sides of any quadrilateral make a parallellogram.do we need the information such that $BP:AP=BQ:CQ=DR:CR=DS:AS$
:oops: :oops: oops.i was puzzled reading the similar looking problem.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Phlembac Adib Hasan
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Re: An interesting problem related to ratio

Unread post by Phlembac Adib Hasan » Mon Feb 06, 2012 2:10 pm

Hint :
Think about similar triangles for easy proof.Complex proof is not so hard,either.
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