document.write( "Question 1197198: Let ABCD be a rectangle and M a point inside it. \r
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Algebra.Com's Answer #830366 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Imagine that the rectangle ABCD lies in the first quadrant;\r\n" );
document.write( "that its vertex A is the origin of the coordinate system,\r\n" );
document.write( "vertex B lies on x-axis and vertex D lies on y-axis.\r\n" );
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document.write( "Let x-dimension of the rectangle be \"a\", and \r\n" );
document.write( "    y-dimension of the rectangle be \"b\".\r\n" );
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document.write( "Let point M has coordinates  M = (x,y).\r\n" );
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document.write( "Then  (MA)^2 + (MC)^2 = (x^2     + y^2) + ((a-x)^2 + (b-y)^2).    (1)\r\n" );
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document.write( "      (MB)^2 + (MD)^2 = ((a-x)^2 + y^2) + (x^2     + (b-y)^2).    (2)\r\n" );
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document.write( "You can see at a first glance that expressions (1) and (2) are equal, since they are identical\r\n" );
document.write( "(the difference is only in the order of addends).\r\n" );
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document.write( "So, the problem is just solved and the required equality is proved.\r\n" );
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