Seven Tangent Circles

Each of the small circles in the figure has radius 1. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the region that surrounds the seven small circles.

Source: NCTM Mathematics Teacher

SOLUTION
area\;of\;surrounding\;region=area\;of\;large\;circle-7\left (area\;of\;small\;circle\right )
=\pi\left (\frac{6}{2}\right )^2-7\left [\pi\left (1\right )^2\right ]
=9\pi-7\pi
=2\pi

Answer: 2\pi

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About mvtrinh

Retired high school math teacher.
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