document.write( "Question 1205840: A circle passes through A and B, and is tangent to line CD. Find its area, in cm^2.\r
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Algebra.Com's Answer #842891 by ikleyn(52805) $\"\"$ $\"About$

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\n" ); document.write( "A circle passes through A and B, and is tangent to line CD. Find its area, in cm^2.
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\n" ); document.write( "\n" ); document.write( " The problem does not tell it, by it is clear from the plot,
\n" ); document.write( " and I will assume it, that AB is parallel to CD.\r
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document.write( "Make a sketch for better understanding.  \r\n" );
document.write( "Let \"r\" be the radius of the circle, in centimeters.\r\n" );
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document.write( "The center of the circle lies on the perpendicular bisector to AB,\r\n" );
document.write( "and the distance from the center to AB is   =  cm.\r\n" );
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document.write( "Therefore, this equlation is hold \r\n" );
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document.write( "    r +  = 10 cm\r\n" );
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document.write( "Our task is to solve it to determine the rasdius r.\r\n" );
document.write( "It is easy. Move r from left side to right\r\n" );
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document.write( "     = 10-r.\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "     = \r\n" );
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document.write( "     = \r\n" );
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document.write( " Cancel  in both sides and simplify\r\n" );
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document.write( "    20r = 100 + 4\r\n" );
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document.write( "    20r = 104\r\n" );
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document.write( "      r =  =  cm = 5.2 cm.\r\n" );
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document.write( "Now the area of the circle is  \r\n" );
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document.write( "     =  = 266.8741 cm^2 (rounded).    ANSWER\r\n" );
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