document.write( "Question 979932: If a circle has a diameter of 10 units and passes through the coordinates (5, 0), which of the coordinates cannot also lie on the circle's boundary, if the center of the circle must have integer coordinates?\r
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Algebra.Com's Answer #601338 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We don't need to do it like the other tutor suggests. We don't even need to\r\n" );
document.write( "know the equation of a circle.  You may not have even studied that yet,\r\n" );
document.write( "anyway.  We just plot those points and draw three circles with diameter 10\r\n" );
document.write( "(radius 5) with centers (0,0), (5,5) and (10,5):\r\n" );
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document.write( "So we just look and see that a circle with a diameter of 10 units and \r\n" );
document.write( "passes through the coordinates A,C,D, and E, and all three circles \r\n" );
document.write( "have centers with integer coordinates.\r\n" );
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document.write( "So if one of those points can't lie on a circle's boundary\r\n" );
document.write( "with integer coefficients and radius 5, it would have to be B(0,0).\r\n" );
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document.write( "We can quit here and figure that the answer can only be B(0,0).\r\n" );
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document.write( "However we haven't really shown that B(0,0) can't lie on a circle's boundary\r\n" );
document.write( "with integer coefficients and radius 5.  We've only gotten it by elimination.\r\n" );
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document.write( "Let's draw a circle (in red) with radius 5 that goes through B(0,0)\r\n" );
document.write( "and also through (5,0).  Let's also draw in two radii and label \r\n" );
document.write( "the center O. \r\n" );
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document.write( "That forms an equilateral triangle, because all sides are 5 units long.\r\n" );
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document.write( "Since we know that the altitude of an equilateral triangle is √3/2 times\r\n" );
document.write( "the length of a side of the equilateral_triangle, we know that the y-\r\n" );
document.write( "coordinate of the center O is 5 times √3/2, and is irrational.\r\n" );
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document.write( "And it's the same with the only other circle we could draw with radius\r\n" );
document.write( "5 that goes through B(0,0) and (5,0). \r\n" );
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document.write( "Edwin
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