IMO 2021 Shortlist G5
Let ABCD be a cyclic quadrilateral whose sides have pairwise different lengths. Let O be the circumcentre of ABCD. The i...
Category: Geometry
Problem
Let ABCD be a cyclic quadrilateral whose sides have pairwise different lengths. Let O be the circumcentre of ABCD. The internal anglebisectors of =ABC and =ADC meet AC at B1 and D1, respectively. Let OB be the centre of the circle which passes through B and is tangent to AC at D1. Similarly,let OD be the centre of the circle which passes through D and is tangent to AC at B1. Assume that BD1 k DB1. Prove that O lies on the line OBOD.