I’m watching this video https://youtu.be/8YDw4YxT-FM giving a smart proof. Check from 12:23 the question 
And 15:50 the solution by promoting it to 3D : 
But I’m not so convinced. Is there a more strict proof?
2026-04-19 03:18:39.1776568719
How to prove if 3 circles intersecting with each others the 3 common chords will cross the same point?
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