How do you do this math question?

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<p>Diagram: <a href="http://s24.postimage.org/m4bjj15qd/3_2_2013_4_34_53_PM.jpg%5B/url%5D"&gt;http://s24.postimage.org/m4bjj15qd/3_2_2013_4_34_53_PM.jpg&lt;/a&gt;&lt;/p>

<p>The diagram to the left shows four identical circles with a total circumference of 16pi. </p>

<p>Assuming that each circle is tangent to two of the other circles in the diagram, what is the circumference of the smallest circle that completely contains all four circles?</p>

<p>Answer: 4pi(1+√2)</p>

<p>How do you do this?</p>

2

<p>You can find r=2 easily by saying C for each circle=2πr and multiplying by 4 to get the equation 8πr=16. Now consider the square formed by the centers of the four circles. The radius of the solution circle will go from the center of the square through a vertex until it intersects the far side of the circle. So R=2+half the diagonal of the square. The square has side length 4 (twice the radius of a smaller circle), so half of its diagonal is 2sqrt(2). Now C=2πR=2π(2+2sqrt(2))=4π(1+sqrt(2))</p>