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Jun 13, 2023 at 10:07 comment added Nandakumar R Thanks for the correction. Shall mark this question as solved and look forward to a settlement to the perimeter issue.
Jun 12, 2023 at 18:51 comment added Fedor Petrov I am afraid that for perimeters things are different. The derivative involves the angle between the chord and the tangent
Jun 12, 2023 at 18:03 vote accept Nandakumar R
Jun 12, 2023 at 18:03 comment added Nandakumar R Thanks very much. The same argument seems to prove the other claim as well - A_1B_1 is got by slightly rotating AB about O. Arcs AA_1 and BB_1 will not be of same length if O is not a center of symmetry so both chords AB and A_1B_1 wont be perimeter bisectors.
Jun 12, 2023 at 17:41 history answered Fedor Petrov CC BY-SA 4.0