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IMOC 2019 G2 (4 midpoints are concyclic, orthocenter, symmetry wrt line)

Source: https://artofproblemsolving.com/community/c6h1958463p13536764

March 21, 2020
geometrysymmetryorthocentermidpointsConcyclic

Problem Statement

Given a scalene triangle △ABC\vartriangle ABC with orthocenter HH. The midpoint of BCBC is denoted by MM. AHAH intersects the circumcircle at D≠AD \ne A and DMDM intersects circumcircle of △ABC\vartriangle ABC at T≠DT\ne D. Now, assume the reflection points of MM with respect to AB,AC,AHAB,AC,AH are F,E,SF,E,S. Show that the midpoints of BE,CF,AM,TSBE,CF,AM,TS are concyclic. https://3.bp.blogspot.com/-v7D_A66nlD0/XnYNJussW9I/AAAAAAAALeQ/q6DMQ7w6QtI5vLwBcKqp4010c3XTCj3BgCK4BGAYYCw/s1600/imoc2019g2.png
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