document.write( "Question 1084921: the center of a circle is at (4,2) and its radius is 5. find the length of the chord which is bisected at (2,-1).
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Algebra.Com's Answer #699088 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "the center of a circle is at (4,2) and its radius is 5. find the length of the chord which is bisected at (2,-1).
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\n" ); document.write( "\n" ); document.write( "Below I placed much simpler solution.\r
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document.write( "1.  Make a sketch to follow my arguments.\r\n" );
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document.write( "    Let the point O = (4,2) be the center of the circle,\r\n" );
document.write( "    and let the point A = (2,-1) bisects our chord.\r\n" );
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document.write( "    Let B  and C be the endpoints of the chord.\r\n" );
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document.write( "2.  Then  =  + ,   or\r\n" );
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document.write( "    For |OC| you have   = 25  and  for  |OA| you have \r\n" );
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document.write( "      =  =  = .\r\n" );
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document.write( "    Therefore,   =  = 12.\r\n" );
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document.write( "    Then |AC| =  = ,\r\n" );
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document.write( "         and  |BC| = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The length of the chord is $\"4%2Asqrt%283%29\"$ .\r
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