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A delicious geometry in Taiwan TST

Source: 2023 Taiwan TST Round 2 Mock P3

April 7, 2023
geometry

Problem Statement

Let Ω\Omega be the circumcircle of an acute triangle ABCABC. Points DD, EE, FF are the midpoints of the inferior arcs BCBC, CACA, ABAB, respectively, on Ω\Omega. Let GG be the antipode of DD in Ω\Omega. Let XX be the intersection of lines GEGE and ABAB, while YY the intersection of lines FGFG and CACA. Let the circumcenters of triangles BEXBEX and CFYCFY be points SS and TT, respectively. Prove that DD, SS, TT are collinear. Proposed by kyou46 and Li4.
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