MathDB
Coordbash? Call me crazy... (BMT 2019 Geo #8)

Source:

May 18, 2019

Problem Statement

Let △ABC \triangle ABC be a triangle with AB=13 AB = 13 , BC=14 BC = 14 , and CA=15 CA = 15 . Let G G denote the centroid of △ABC \triangle ABC , and let GA G_A denote the image of G G under a reflection across BC‾ \overline{BC} , with GB G_B the image of G G under a reflection across AC‾ \overline{AC} , and GC G_C the image of G G under a reflection across AB‾ \overline{AB} . Let OG O_G be the circumcenter of △GAGBGC \triangle G_AG_BG_C and let X X be the intersection of AOG‾ \overline{AO_G} with BC‾ \overline{BC} . Let Y Y denote the intersection of AG‾ \overline{AG} with BC‾ \overline{BC} . Compute XY XY .
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