IMO Shortlist 2010 problem G6
Dodao/la:
arhiva23. lipnja 2013. The vertices

of an equilateral triangle

lie respectively on the sides

of an acute-angled triangle

Prove that the incenter of triangle

lies inside triangle

Proposed by Nikolay Beluhov, Bulgaria
%V0
The vertices $X, Y , Z$ of an equilateral triangle $XYZ$ lie respectively on the sides $BC, CA, AB$ of an acute-angled triangle $ABC.$ Prove that the incenter of triangle $ABC$ lies inside triangle $XYZ.$
Proposed by Nikolay Beluhov, Bulgaria
Izvor: Međunarodna matematička olimpijada, shortlist 2010