1983 AHSME Problem 29

A point P lies in the same plane as a given square of side 1. Let the vertices of the square, taken counterclockwise, be A, B, C and D. Also, let the distances from P to A, B and C, respectively, be u, v and w. What is the greatest distance that P can be from D if u^2 + v^2 = w^2?

\textbf{(A)}\ 1 + \sqrt{2}\qquad \textbf{(B)}\ 2\sqrt{2}\qquad \textbf{(C)}\ 2 + \sqrt{2}\qquad \textbf{(D)}\ 3\sqrt{2}\qquad \textbf{(E)}\ 3+\sqrt{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.