2024 SSMO Accuracy Round Problems/Problem 8

Problem

$ABCD$ is a convex cyclic quadrilateral with $AB = 2, BC = 5, CD = 10,$ and $AD = 11.$ Let $W, Y, X,$ and $Z$ be the midpoints of sides $AB, BC, CD,$ and $DA$ respectively. If $|(WX^2-YZ^2)|$ can be expressed as $\frac{m}{n},$ for relatively prime positive integers $m$ and $n,$ find $m+n.$

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2024 SSMO Accuracy Round Problems/Problem 8

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