We consider the third problem from International Mathematical Olympiad -2021.
Useful links (in Russian):
Isogonal conjugation in quadrilaterals:
1. Article by A. Utkin in Kvant: http://www.mathnet.ru/links/bba3fda047ae64a5e8b4b716cd4694c2/kvant804.pdf
2. Problems collection by A. Kushnir and A. Sokolov: http://math.mosolymp.ru/upload/files/2020/khamovniki/geom-10/2020-02-18-isogonal-conjugacy-in-a-quadrilateral.pdf
Isogonality lemma:
Article by A. Kulikova and D. Prokopenko in Kvant: https://geometry.ru/articles/isogonal_theorem_kvant_04_05.pdf
