IMO 2021 Shortlist G7
A point D is chosen inside an acute-angled triangle ABC with AB ą AC so that =BAD “ =DAC. A point E is constructed on th...
Category: Geometry
Problem
A point D is chosen inside an acute-angled triangle ABC with AB ą AC so that =BAD “ =DAC. A point E is constructed on the segment AC so that =ADE “ =DCB. Similarly, a point F is constructed on the segment AB so that =ADF “ =DBC. A point X is chosen on the line AC so that CX “ BX. Let O1 and O2 be the circumcentres of the triangles ADC and DXE. Prove that the lines BC, EF, and O1O2 are concurrent.