2008 Fermat Problem 23

Square PQRS has side length 4 m. Point U is on PR with PR = 4UR. A circle centered at U touches two sides of the square. PW is a tangent to the circle, with W on QR. The length of PW, to the nearest thousandth of a metre, is

\textbf{(A)}\ 4.123 \text{ m}\quad \textbf{(B)}\ 4.472 \text{ m}\quad \textbf{(C)}\ 4.685 \text{ m}\quad \textbf{(D)}\ 4.726 \text{ m}\quad \textbf{(E)}\ 4.767 \text{ m}

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