Concentric Circles

The circles in the figure are concentric. The chord is tangent to the inner circle and has length 12. What is the area of the non-shaded region?
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Source: NCTM Mathematics Teacher, November 2006

SOLUTION
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x^2+6^2=r^2
r^2-x^2=36
area of large circle =\pi r^2
area of inner circle =\pi x^2
area of non-shaded region=area of large circle – area of inner circle
=\pi r^2-\pi x^2
=\pi(r^2-x^2)
=\pi 36

Answer: 36\pi

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About mvtrinh

Retired high school math teacher.
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