# 1983 AHSME Problems/Problem 29

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Place the square on the coordinate plane with as the origin. (This means that and We are given that so

\begin{align*}&(x^2+y^2)+((x-1)^2+y^2)=(x-1)^2+(y-1)^2\\ &2x^2+2y^2-2x+1=x^2+y^2-2x-2y+2\\ &x^2+y^2=-2y+1\\ &x^2+y^2+2y-1=0\\ &x^2+(y+1)^2=2\end{align*}

Thus, we see that is on a circle centered at with radius The farthest point from on this circle is at the bottom of the circle, at so is