"implies Santa Claus exists when preceded by itself quoted"

by math_explorer, Mar 6, 2011, 5:28 AM

APMO2010.4. Let $ABC$ be an acute angled triangle satisfying the conditions $AB>BC$ and $AC>BC$. Denote by $O$ and $H$ the circumcentre and orthocentre, respectively, of the triangle $ABC.$ Suppose that the circumcircle of the triangle $AHC$ intersects the line $AB$ at $M$ different from $A$, and the circumcircle of the triangle $AHB$ intersects the line $AC$ at $N$ different from $A.$ Prove that the circumcentre of the triangle $MNH$ lies on the line $OH$.

Let's see if things have changed.
geo problem
geometry

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Eh? Don't get the title.

by chaotic_iak, Mar 6, 2011, 3:56 PM

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You're supposed to use it to prove that Santa exists.

Meanwhile I may or may not have reduced the problem to proving that $OM_BM_C$ and $HP_CP_B$ are perspective.
This post has been edited 1 time. Last edited by math_explorer, Mar 7, 2011, 12:35 AM

by math_explorer, Mar 7, 2011, 12:33 AM

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