document.write( "Question 166147: Find the radius of a circle with center at (4,1) if a chord of length 4 times square root of 2 is bisected at (7,4). \n" ); document.write( "

Algebra.Com's Answer #122594 by Edwin McCravy(20055) $\"\"$ $\"About$

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Find the radius of a circle with center at (4,1) if a chord of length 4 times square root of 2 is bisected at (7,4).
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document.write( "Let O be the center of the circle (4,1).\r\n" );
document.write( "Let P be the point (7,4), \r\n" );
document.write( "Let A and B be the endpoints of the chord,\r\n" );
document.write( "so the chord is the segment AB. Draw the\r\n" );
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document.write( "Draw in OA and OP:\r\n" );
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document.write( "We need to find the length of OA since it \r\n" );
document.write( "is a radius of the circle.\r\n" );
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document.write( "Triangle OPA is a right triangle, since if a\r\n" );
document.write( "bisector of a chord passes through the center of\r\n" );
document.write( "a circle, then it is perpendicular to the chord.\r\n" );
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document.write( "We are given that chord AB has length ,\r\n" );
document.write( "and since P bisects it, then AP is half that length\r\n" );
document.write( "or .\r\n" );
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document.write( "Next we will find the length of OP by use of the\r\n" );
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document.write( "using the given coordinates of O(4,1) and P(7,4):\r\n" );
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document.write( "Now by the Pythagorean theorem,\r\n" );
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document.write( "And since OA is a radius, the circle has \r\n" );
document.write( "radius .\r\n" );
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document.write( "Edwin

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