2021 WSMO Team Round/Problem 15

Problem

Let $ABCD$ and $DEFG$ (vertices labelled clockwise) be squares that intersect exactly once and with areas $1011^2$ and $69^2$ respectively. There exists a constant $M$ such that $CE+AG>M$ where $M$ is maximized. Find $M.$

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2021 WSMO Team Round/Problem 15

Problem

Solution