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 ?
Some thoughts I had:
1) Given a pair of vertices I could construct an ellipse with P as a point on the ellipse.
2) From the equality . I think that I have to consider the case where the angle between u and v is . In this case I would have and .
That being said,I still fail to come at a concrete solution of the problem,it might be that none of my thoughts are right...