document.write( "Question 1156833: A chord 6 cm long is 2 cm from the center of a circle. How long is a chord that is 1 cm
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Algebra.Com's Answer #779601 by ikleyn(52779) $\"\"$ $\"About$

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document.write( "Make a sketch.\r\n" );
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document.write( "Draw the perpendicular radius to the first chord.\r\n" );
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document.write( "Find right angled triangle in the sketch.\r\n" );
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document.write( "For this right angled triangle, write the Pythagorean formula\r\n" );
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document.write( "    r^2 = d^2 + L^2,    (1)\r\n" );
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document.write( "where r is the radius of the circle, d is the distance of the chord from the center of the circle \r\n" );
document.write( "and L is half the chord's length.\r\n" );
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document.write( "Then from (1) you get\r\n" );
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document.write( "    r^2 = 2^2 + (6/2)^2 = 4 + 3^2 = 4 + 9 = 13.\r\n" );
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document.write( "Thus the radius of the circle is  .\r\n" );
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document.write( "Now write equation (1) for the chord, which is 1 cm from the center of the same circle\r\n" );
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document.write( "    13 = 1^2 + (x/2)^2 \r\n" );
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document.write( "where x the length of this chord.\r\n" );
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document.write( "You then get\r\n" );
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document.write( "    (x/2)^2 = 13 - 1 = 12;\r\n" );
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document.write( "    x/2 =  = \r\n" );
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document.write( "ANSWER.  The length of the cord is   = 6.928 centimetres.\r\n" );
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