Problem

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Tags: geometry, right triangle, Angle Chasing, contests



Let $ABC$ be an isosceles right triangle at $A$ with $AB=AC$. Let $M$ and $N$ be on side $BC$, with $M$ between $B$ and $N,$ such that $$BM^2+ NC^2= MN^2.$$Determine the measure of the angle $\angle MAN.$