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2016-2017 Fall OMO Problem 3

Source:

November 16, 2016
geometry

Problem Statement

In a rectangle ABCDABCD, let MM and NN be the midpoints of sides BCBC and CDCD, respectively, such that AMAM is perpendicular to MNMN. Given that the length of ANAN is 6060, the area of rectangle ABCDABCD is mnm \sqrt{n} for positive integers mm and nn such that nn is not divisible by the square of any prime. Compute 100m+n100m+n.
Proposed by Yannick Yao
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