IMO 2017 Shortlist G7

A onvex quadrilateral ABCD has an ins ribed ir le with enter I. Let Ia, Ib, Ic, and Id be the in enters of the triangles...

IMO 2017 Shortlist G7

Category: Geometry

Problem

A onvex quadrilateral ABCD has an ins ribed ir le with enter I. Let Ia, Ib, Ic, and Id be the in enters of the triangles DAB, ABC, BCD, and CDA, respe tively. Suppose that the ommon external tangents of the ir les AIbId and CIbId meet at X, and the ommon external tangents of the ir les BIaIc and DIaIc meet at Y . Prove that =XIY “ 900 . (Kazakhstan)