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
Školjka