IMO 2024 Shortlist G1

Let ABCD be a cyclic quadrilateral such that AC ă BD ă AD and =DBA ă 90˝ . Point E lies on the line through D parallel t...

IMO 2024 Shortlist G1

Category: Geometry

Problem

Let ABCD be a cyclic quadrilateral such that AC ă BD ă AD and =DBA ă 90˝ . Point E lies on the line through D parallel to AB such that E and C lie on opposite sides of line AD, and AC “ DE. Point F lies on the line through A parallel to CD such that F and C lie on opposite sides of line AD, and BD “ AF. Prove that the perpendicular bisectors of segments BC and EF intersect on the circumcircle of ABCD. (Ukraine)