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Radical axis of circles is concur

Source: Sharygin 2019 Finals Day 2 Grade 9 P4

July 31, 2019
Sharygin 2019 Finals day2 P4Sharygin Geometry Olympiad

Problem Statement

A hexagon A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 has no four concyclic vertices, and its diagonals A1A4A_1A_4, A2A5A_2A_5 and A3A6A_3A_6 concur. Let lil_i be the radical axis of circles AiAi+1Ai−2A_iA_{i+1}A_{i-2} and AiAi−1Ai+2A_iA_{i-1}A_{i+2} (the points AiA_i and Ai+6A_{i+6} coincide). Prove that li,i=1,⋯ ,6l_i, i=1,\cdots,6, concur.
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