document.write( "Question 353422: three circles, each with a radius of 6 inches, are externally tangent to each other. What is the area if the region which is the exterior of all three circles but which is bounded by the three circles? \n" ); document.write( "

Algebra.Com's Answer #252564 by Edwin McCravy(20055) $\"\"$ $\"About$

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three circles, each with a radius of 6 inches, are externally tangent to each other. What is the area if the region which is the exterior of all three circles but which is bounded by the three circles?
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document.write( "We want the area of the figure bounded by the red arcs:\r\n" );
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document.write( "Draw equilateral triangle ABC by connecting the centers\r\n" );
document.write( "of the three circles:\r\n" );
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document.write( "Each of the interior angles of equilateral triangle ABC\r\n" );
document.write( "is 60° or  radians.  So in particular angle DAF is \r\n" );
document.write( "60° or  radians.  \r\n" );
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document.write( "Sector ADF has area given by the formula\r\n" );
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document.write( "  where  is in radians\r\n" );
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document.write( "The other two sectors CEF and BDE are congruent to sector ADF \r\n" );
document.write( "and so they also have area , so the three sectors together \r\n" );
document.write( "have a total area of  or .\r\n" );
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document.write( "An equilateral triangle has area .\r\n" );
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document.write( "Each side of equilateral triangle ABC is , so its area\r\n" );
document.write( "is given by\r\n" );
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document.write( "To find the area bounded by the red arcs, we subtract the total \r\n" );
document.write( "area of the three sectors  from the area of the \r\n" );
document.write( "equilateral triangle ABC, and so the final answer is\r\n" );
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document.write( "Edwin

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