IMO 2024 Shortlist G4

Let ABCD be a quadrilateral with AB parallel to CD and AB ă CD. Lines AD and BC intersect at a point P. Point X ‰ C on t...

IMO 2024 Shortlist G4

Category: Geometry

Problem

Let ABCD be a quadrilateral with AB parallel to CD and AB ă CD. Lines AD and BC intersect at a point P. Point X ‰ C on the circumcircle of triangle ABC is such that PC “ PX. Point Y ‰ D on the circumcircle of triangle ABD is such that PD “ PY . Lines AX and BY intersect at Q. Prove that PQ is parallel to AB. (Ukraine)