2020 USOMO Problems
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[hide]Day 1
Problem 1
Let be a fixed acute triangle inscribed in a circle with center . A variable point is chosen on minor arc of , and segments and meet at . Denote by and the circumcenters of triangles and , respectively. Determine all points for which the area of triangle is minimized.
Problem 2
An empty cube is given, and a grid of square unit cells is drawn on each of its six faces. A beam is a rectangular prism. Several beams are placed inside the cube subject to the following conditions: