2022 SSMO Relay Round 3 Problems/Problem 2

Problem

Let $T=TNYWR$ . In cyclic quadrilateral $ABCD,$ $\angle{BAD}=60^{\circ},$ and $BC=CD=T.$ If $AB$ is a positive integer, find twice the median of all (not necessarily distinct) possible values of $AB$ .

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2022 SSMO Relay Round 3 Problems/Problem 2

Problem

Solution