The inscribed circle ω of the triangle ABC touches its sides BC,CA, and AB at the points D,E, and F, respectively. Let the points X,Y, and Z of the circle ω be diametrically opposite to the points D,E, and F, respectively. Line AX,BY and CZ intersect the sides BC,CA and AB at the points D′,E′ and F′, respectively. On the segments AD′,BE′ and CF′ noted the points X′,Y′ and Z′, respectively, so that D′X′=AX, E′Y′=BY, F′Z′=CZ. Prove that the points X′,Y′ and Z′ coincide. geometryequal segmentsUkrainian TYM