Four Circles

In the diagram, two of the three dark shaded circles have diameters of 4 units, and the third has a diameter of 2. What must be the length of the diameter of the white shaded circle to make the sum of the dark shaded areas A,B, and C equal to the white shaded area?
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Source: NCTM Mathematics Teacher, February 2006

SOLUTION
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area of A + area of B + area of C = area of white circle – area of D – area of E – area of F
(area of A + area of D) + (area of B + area of E) + (area of C + area of F) = area of white circle
\pi 2^2+\pi 2^2+\pi 1^2=\pi x^2 where x is the radius of the white circle
9\pi=\pi x^2
x^2=9
x=\pm 3
Diameter of white circle = 2\times 3=6

Answer: 6 units

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About mvtrinh

Retired high school math teacher.
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