Talk:2023 IMO Problems/Problem 6

According my humble opinion, the proof is not completed. It shows only the existence of a radical centre, fact that is normal among three circles not belonging to a sheaf, but in this case it must be proved that the radical centre is exactly one of the two common point, because, generally, a radical centre does not belong to any of the three intersecting circles! In other words, it is necessary to show that P (and Q) stands on all the three circles, that is its power is null with respect to all of them (and not positive, as it occurs generally). Equal power does not mean null power !