[gniv]

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."

[gus_massa]

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.