Question 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 $u^2+v^2=w^2?$