RU-ALLRUSSIAN 1977 Problem 3
(1) The triangle ABC is inscribed in a circle. D is the midpoint of the arc BC (not containing A), similarly E and F. Show that the hexagon formed by the intersection of ABC and DEF has its main diagonals parallel to the sides of ABC and intersecting in a single point.
(2) EF meets AB at X and AC at Y. Prove that AXIY is a rhombus, where I is the center of the circle inscribed in ABC.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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