document.write( "Question 37105This question is from textbook geometry
\n" ); document.write( ": a) Find the radii of the circles x^2 + y^2 = 2 and (x-3)^2 + (y-3)^2 = 32
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Algebra.Com's Answer #22805 by AnlytcPhil(1807)\"\" \"About 
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a) Find the radii of the circles x² + y² = 2 and (x-3)² + (y-3)² = 32\r\n" );
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document.write( "The circle with center (h,k) has equation (x-h)² + (y-k)² = r²\r\n" );
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document.write( "If we write the first circle's equation as\r\n" );
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document.write( "                                          (x-0)² + (y-0)² = 2\r\n" );
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document.write( "we see that it has center (h,k) = (0,0) and radius r = Ö2   \r\n" );
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document.write( "From the second circle's equation         (x-3)² + (y-3)² = 32\r\n" );
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document.write( "we see that it has center (h,k) = (3,3) and radius Ö32 = Ö16·2 = 4Ö2\r\n" );
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document.write( "b) Find the distance between the centers of the circles\r\n" );
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document.write( "We use the distance formula, which says that the distance between two\r\n" );
document.write( "points (x1, y1) and (x2, y2) is\r\n" );
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document.write( "                               _______________________\r\n" );
document.write( "                          d = Ö(x2 - x1)² + (y2 - y1)²                         \r\n" );
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document.write( "So the distance between (x1,y1) = (0,0) and (x2,y2) = (3,3) is\r\n" );
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document.write( "                          d = Ö(3 - 0)² + (3 - 0)²\r\n" );
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document.write( "                          d = Ö3² + 3² \r\n" );
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document.write( "                          d = Ö9 + 9\r\n" );
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document.write( "                          d = Ö18 \r\n" );
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document.write( "                          d = Ö9·2     \r\n" );
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document.write( "                          d = 3Ö2\r\n" );
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document.write( "c) Explain why the circles must be internally tangent\r\n" );
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document.write( "Because the distance between their centers plus the radius of the small\r\n" );
document.write( "circle equals the radius of the large circle, since\r\n" );
document.write( "                       _    _     _ \r\n" );
document.write( "                     3Ö2 + Ö2 = 4Ö2                 \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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