document.write( "Question 1016836: 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) \n" ); document.write( "

Algebra.Com's Answer #633210 by ikleyn(52839) $\"\"$ $\"About$

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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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document.write( "1. Make a sketch.\r\n" );
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document.write( "   Draw the circle, the chord and the bisection point.\r\n" );
document.write( "   Draw the radii of the circle to the endpoints of the chord.\r\n" );
document.write( "   Draw the line from the center of the circle to the bisection point at the chord.\r\n" );
document.write( "   This line is the perpendicular to the chord.\r\n" );
document.write( "   Do you understand why? - Because it is the median in the isosceles triangle.\r\n" );
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document.write( "   Therefore, the plan of the solution is:\r\n" );
document.write( "      a) find the length of this perpendicular, and then\r\n" );
document.write( "      b) find the length of the leg of the right-angled triangle, which is exactly half of the length of the chord; and then\r\n" );
document.write( "      c) double the length of that leg.\r\n" );
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document.write( "2. Below find how this plan is implemented.\r\n" );
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document.write( "a) The distance from the center (4,2) to the point (2,-1) is\r\n" );
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document.write( "    =  =  = .\r\n" );
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document.write( "b) The length of the leg of the right-angled triangle is\r\n" );
document.write( "    =  =  = .\r\n" );
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document.write( "c) The length of the chord is  = .\r\n" );
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document.write( "Answer. The length of the chord is .\r\n" );
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