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USAM(inimize)OOO

Source: 2020 USOMO Problem 1

June 21, 2020
minimizeUSAMOgeometryOlympiadOlympiad Geometryarea of a triangleUSOMO

Problem Statement

Let ABCABC be a fixed acute triangle inscribed in a circle ω\omega with center OO. A variable point XX is chosen on minor arc ABAB of ω\omega, and segments CXCX and ABAB meet at DD. Denote by O1O_1 and O2O_2 the circumcenters of triangles ADXADX and BDXBDX, respectively. Determine all points XX for which the area of triangle OO1O2OO_1O_2 is minimized.
Proposed by Zuming Feng
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