FERMAT 2008 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

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Answer Choices
A. 4.123\:m
B. 4.472\:m
C. 4.685\:m
D. 4.726\:m
E. 4.767\:m