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2024 SSMO Relay Round 2 Problems/Problem 3

Problem

Let $T = TNYWR.$ A point $P$ is randomly chosen inside the square with vertices $A = (0,0), B = (0,T), C = (T,T),$ and $D = (T,0)$. Find the perimeter of the set $S$ containing all points $P$ for which $AP + CP \ge BP + DP.$

Solution

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