IMO 2021 Shortlist G2

Let ABCD be a convex quadrilateral circumscribed around a circle with centre I. Let ω be the circumcircle of the triangl...

IMO 2021 Shortlist G2

Category: Geometry

Problem

Let ABCD be a convex quadrilateral circumscribed around a circle with centre I. Let ω be the circumcircle of the triangle ACI. The extensions of BA and BC beyond A and C meet ω at X and Z, respectively. The extensions of AD and CD beyond D meet ω at Y and T, respectively. Prove that the perimeters of the (possibly self-intersecting) quadrilaterals ADTX and CDY Z are equal.