In one mathes lecture this week, a professor suddenly threw out a random high school geometry question on our quiz for a bonus (the topic test was on central limit theorem), and i had no idea it was coming i dont know if my solution is correct, but this is the problem (if i remember correctly):

If $ \displaystyle A_1,A_2...A_n$are the vertices of a regular plane polygon with n sides and O is its centre, show that:

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