document.write( "Question 1202298: Find the radius of a circle with center at (4,1) if a chord of length 4√2 is bisected at (7,4) \n" ); document.write( "

Algebra.Com's Answer #837024 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the radius of a circle with center at (4,1)
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document.write( "Make a sketch.\r\n" );
document.write( "In your sketch, find a right-angled triangle, which has the vertices OXY, where\r\n" );
document.write( "O  is the center of the circle;  X  is the midpoint of the chord and \r\n" );
document.write( "Y  is  one of the two intersection points of the chord and the circle.\r\n" );
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document.write( "The leg XY of this triangle has the length , half of the leg\r\n" );
document.write( "of the chord; the leg OX is the vector with coordinates (3,3) = (7-4,4-1).\r\n" );
document.write( "The length of this leg OX is  .\r\n" );
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document.write( "The radius \"r\" of the circle is the hypotenuse of this triangle\r\n" );
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document.write( "     =  +  = 4*2 + 9*2 = 8 + 18 = 26.\r\n" );
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document.write( "ANSWER.  The radius of the circle is  r =  units.\r\n" );
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