### European Girls 2012-19 (EGMO) 15p

geometry problems from European Girls' Mathematical Olympiad  (EGMO)
with aops links in the names

2012 - 2019

EGMO  2012 / 1
Let ABC be a triangle with circumcentre O. The points D, E and F lie in the interiors of the sides BC, CA and AB respectively, such that DE is perpendicular to CO and DF is perpendicular to BO. Let K be the circumcentre of triangle AFE. Prove that the lines DK and BC are perpendicular.