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Found problems: 1

2019 Sharygin Geometry Olympiad, 8
Tags: Sharygin 2019 Finals day2 P4 , Sharygin Geometry Olympiad
A hexagon $A_1A_2A_3A_4A_5A_6$ has no four concyclic vertices, and its diagonals $A_1A_4$, $A_2A_5$ and $A_3A_6$ concur. Let $l_i $ be the radical axis of circles $A_iA_{i+1}A_{i-2} $ and $A_iA_{i-1}A_{i+2} $ (the points $A_i $ and $A_{i+6} $ coincide). Prove that $l_i, i=1,\cdots,6$, concur.