IMO 2018 Shortlist G6

A onvex quadrilateral ABCD satises AB ¨ CD “ BC ¨ DA. A point X is hosen inside the quadrilateral so that =XAB “ =XCD a...

imomathematicsolympiadshortlistgeometry

IMO 2018 Shortlist G6

Category: Geometry

Problem

A onvex quadrilateral ABCD satises AB ¨ CD “ BC ¨ DA. A point X is hosen inside the quadrilateral so that =XAB “ =XCD and =XBC “ =XDA. Prove that =AXB` =CXD “ 180˝ . (Poland)