1983 AHSME Problems/Problem 29
A point lies in the same plane as a given square of side . Let the vertices of the square, taken counterclockwise, be and . Also, let the distances from to and , respectively, be and . What is the greatest distance that can be from if ?
Place the square in the -plane with as the origin, so that and We are given that so
Thus we see that lies on a circle centered at with radius The farthest point from on this circle is at the bottom of the circle, at in which case is