Two-Time IMO Gold Medalist Becomes President of Romania

Re:Two-Time IMO Gold Medalist Becomes President of Romania by gniv on Monday May 19, 2025 @06:31AM (#44028274)

If you like geometry I recommend problem 2 from that 1987 IMO. Simple formulation, elegant solution. Hard, but not crazy hard imo.

"In an acute-angled triangle ABC the interior bisector of the angle A intersects BC at L and intersects the circumcircle of ABC again at N. From point L perpendiculars are drawn to AB and AC, the feet of these perpendiculars being K and M respectively. Prove that the quadrilateral AKNM and the triangle ABC have equal areas."

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Re:Two-Time IMO Gold Medalist Becomes President of Romania by gus_massa on Wednesday May 21, 2025 @06:51AM (#44050123)

I draw it. https://imgur.com/a/W3RH0C2 It's obviously not a proof, but GeoGebra agree the areas are equal :)

PS: Is it possible to link to GeoGebra (or something similar) without an account? I have the ggb file in my desktop.

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