2020 USAMO Problems/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.
Let be midpoint Let be midpoint and are the bases of perpendiculars dropped from and respectively.
The area of is minimized if because email@example.com, vvsss