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IMO 1985-5

Posted: Sun Feb 12, 2012 9:17 pm
by Phlembac Adib Hasan
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 $\angle OMB=90^0$.

Re: IMO 1985-5

Posted: Sun Feb 12, 2012 9:52 pm
by sourav das
I think this is one of the most beautiful problems having so many solutions.....