Send it to more math professionals and see what they will say. Wish you are right.

Well unfortunately, I have yet to email a professional but a guy knowing about this paradox told me that my answer was not wrong, but not correct either, because as per what this paradox said, how to pick a chord at random was ambiguous, and there was no correct answer, but nvm, I will write a math thesis making use of my solution, and it will be published in the next week.