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2024 SSMO Relay Round 4 Problems/Problem 2

Problem

Let $T = TNYWR.$ Regular octagon $OLYMPIAD$ is perfectly inscribed within Circle $Q$. Circle $Q$ has area $T\pi$. If the area of octagon $OLYMPIAD$ is $a\sqrt{b},$ for squarefree $b,$ find $a+b.$

Solution

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