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2024 SSMO Relay Round 2 Problems/Problem 1

Problem

In a regular hexagon $ABCDEF$, let $X$ be a point inside the hexagon such that $XA=XB=3.$ If the area of the hexagon is $6\sqrt{3}$, then $XE^2 = a+b\sqrt{c},$ for squarefree $c$. Find $a+b+c$.

Solution

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