IMO 1985-5

Discussion on International Mathematical Olympiad (IMO)
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Phlembac Adib Hasan
Joined:Tue Nov 22, 2011 7:49 pm
IMO 1985-5

Unread post by Phlembac Adib Hasan » Sun Feb 12, 2012 9:17 pm

A circle with center $O$ passes through points $A$ and $C$ and intersects side $AB$ and $BC$ of $\triangle ABC$ at point $K,N$,respectively.The circumcircles of $\triangle ABC$ and $\triangle KBN$ at $B$ and $M$.Prove that $\angle OMB=90^0$.
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sourav das
Joined:Wed Dec 15, 2010 10:05 am

Re: IMO 1985-5

Unread post by sourav das » Sun Feb 12, 2012 9:52 pm

I think this is one of the most beautiful problems having so many solutions.....
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

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