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Lovely geo

Source: Thailand TSTST 2024 P10

July 18, 2024
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle with altitudes AD,BEAD,BE and CFCF. Denote ω1,ω2\omega_1,\omega_2 the circumcircles of △AEB,△AFC\triangle AEB, \triangle AFC, respectively. Suppose the line through AA parallel to EFEF intersects ω1\omega_1 and ω2\omega_2 at PP and QQ, respectively. Show that the circumcenter of △PQD\triangle PQD lies on ADAD
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