IMO Shortlist 2010 problem G6
Dodao/la:
arhiva23. lipnja 2013. The vertices
![X, Y , Z](/media/m/b/a/4/ba44e2f52747046533b7103b6470f4d0.png)
of an equilateral triangle
![XYZ](/media/m/1/3/d/13dab5022dd1d33f3d299852f2f54cfb.png)
lie respectively on the sides
![BC, CA, AB](/media/m/c/f/7/cf7216e218ef8afb7af9284210a1d7d0.png)
of an acute-angled triangle
![ABC.](/media/m/c/b/7/cb77700b4adade65e440645391a8d2ad.png)
Prove that the incenter of triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
lies inside triangle
![XYZ.](/media/m/2/c/4/2c4f0022ccc0b288f61c02a6eb5cf3e6.png)
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