2023 IOQM/Problem 15
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Let ABCD be a unit square. Suppose M and N are points on BC and CD respectively such that the perimeter of triangle MCN is 2. Let O be the circumcentre of triangle MAN and P be the circumcentre of triangle MON. If (OP⁄OA)²= m/n for some relatively prime positive integers m and n, find the value of m + n.
