document.write( "Question 412212: 4 congruent circles, each of which is tangent externally to 2 of the other circles, are circumscribed by a square of area 16. A small circle is then placed in the center so that it is tangent to each of the four circles. Determine the radius of the smallest circle. \n" ); document.write( "

Algebra.Com's Answer #289591 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Since the area of the square is 16 square units, each side of the \r\n" );
document.write( "square is the square root of 16 or 4 units.\r\n" );
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document.write( "This green line: \r\n" );
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document.write( "is also 4 units and goes across both circles on the left.\r\n" );
document.write( "so each of the four larger circles has radius 1.\r\n" );
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document.write( "Now let's draw a diagonal of the square and letter some points:\r\n" );
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document.write( "ABC is a right triangle,\r\n" );
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document.write( "AB=1, BC=1, so by the Pythagorean theorem AC = \r\n" );
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document.write( "and since GH = AC, GH = \r\n" );
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document.write( "CD and FG are both radii of the larger circles so they are 1 each.\r\n" );
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document.write( "Triangle AIH is a right triangle, AI = 4, IH = 4, so by the\r\n" );
document.write( "Pythagorean theorem, diagonal AH = \r\n" );
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document.write( "We add up the parts of the diagonal AH and equate the sum to  \r\n" );
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document.write( "AC + CD + DF + FG + GH =  \r\n" );
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document.write( "Substituting the values for the parts that we know the lengths of:\r\n" );
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document.write( "+1+DF+1+ = \r\n" );
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document.write( "Now we solve for DF\r\n" );
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document.write( "+2+DF = \r\n" );
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document.write( "DF =  \r\n" );
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document.write( "DF is the diameter of small circle E, so its radius\r\n" );
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document.write( "is  or  \r\n" );
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document.write( "Edwin

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