SHARYGIN 2022 Problem 22

Chords $A_1A_2, A_3A_4, A_5A_6$ of a circle $\Omega$ concur at point $O$ . Let $B_i$ be the second common point of $\Omega$ and the circle with diameter $OA_i$ . Prove that chords $B_1B_2, B_3B_4, B_5B_6$ concur.