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copied!<p>Short answer: NO :P (don´t fell bad about it)</p> <p><strong>Long Answer</strong>: Intersecction the areas from the four circles that you mention (max distance between opposite vertex) does not produce a rectangle.<img src="https://i.stack.imgur.com/aezPJ.png" alt="Common area of four circles of radius equal to the rectangle´s diagonal with center in each corner"> Since I´m a bit rusty in geometry I can´t give full mathematical explanation (time constrain for my part), but give you some pseudocode of the procedure with the constrains that you ask (no fancy formulae), valid for any rectangle the wikipeida or a geometry book can fill the gaps.</p> <ul> <li>Find the N,E,S,W vertex (the uppermost, rightmost, lowest and leftmost vertex) this is trivially easy for any rectangle but the axis aligned who can produce oddly assignation of the vertex (see images with examples) <img src="https://i.stack.imgur.com/8decM.png" alt="enter image description here"></li> <li>Find the NE, SE, SW and NW border, this is the line equation <a href="http://en.wikipedia.org/wiki/Line_%28geometry%29" rel="nofollow noreferrer" title="example in wikipeida">in wikipedia</a> or another <a href="http://www.cut-the-knot.org/Curriculum/Calculus/StraightLine.shtml" rel="nofollow noreferrer" title="another web">link</a>, again should be easy, but the axis aligned border should be analized carefully <a href="http://en.wikipedia.org/wiki/Linear_equation" rel="nofollow noreferrer" title="wikipeida link">because those generate another type of ecuation/restriction</a>.</li> <li><p>Check if your point is on the "right side" of the border <a href="http://en.wikipedia.org/wiki/Inequality_%28mathematics%29" rel="nofollow noreferrer" title="Wikipedia Link">see inequality as mathematical term</a>, only a point <strong>inside your rectangle</strong> satisfy the four restrictions as you can see in the image attached. <img src="https://i.stack.imgur.com/yRatC.png" alt="for each "border" the green area present a valid place for the point"></p></li> <li><p>my apologies if I have overlook some command of java.geom that can accomplish this task</p></li> </ul> <p>I hope this help with your endevour</p>

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