Olympiad Corner 費馬最後定理 ((((一一一一))))

∠ARN =180 o −∠BAC. So ∠MPN + ∠MSN =180 o. Then, M, N, S, P are concyclic. In the later case, ∠MPN = ∠PQR + ∠PRQ = ∠AQM + ∠ARN = ∠BAC = ∠MSN. So again M, N, S, P are concyclic. Similarly, if the line does not intersect side BC, there are 2 cases

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