document.write( "Question 1059003: Let point A be a point on the circle whose equation is (x - 3)^2 + (y + 4)^2 = 50. How many different points X lie on the circle so that the chord AX has integer length? \n" ); document.write( "

Algebra.Com's Answer #674336 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "This is a trick question.  The answer is 28.  What Iklyn solved \r\n" );
document.write( "instead was this problem:\r\n" );
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document.write( "Let A and B be endpoints of a diameter of a circle whose diameter \r\n" );
document.write( "has length . How many points on the circumference of the \r\n" );
document.write( "circle are such that right triangle AXB has legs AX and BX whose \r\n" );
document.write( "lengths are both integers.\r\n" );
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document.write( "But that's not the given problem.\r\n" );
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document.write( "In solving the given problem, there is nothing to calculate but \r\n" );
document.write( "the diameter of the circle.  \r\n" );
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document.write( "The diameter of ANY circle is the longest possible chord of that \r\n" );
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document.write( "Chords of ANY length greater than 0 and less than or equal to the\r\n" );
document.write( "diameter of ANY circle can be drawn from ANY point on that circle.\r\n" );
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document.write( "Here the radius is  and the diameter is  \r\n" );
document.write( "which is approximately 14.14 \r\n" );
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document.write( "The chords must be of integer length.  Therefore chords of lengths\r\n" );
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document.write( " 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\r\n" );
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document.write( "can all be drawn from any point on that circle each in 2 ways,\r\n" );
document.write( "clockwise or counter-clockwise.\r\n" );
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document.write( "so the answer is 28.\r\n" );
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document.write( "  :)\r\n" );
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document.write( "Edwin

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