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An arbelos is the region bordered by three mutually tangent circles with co-linear centers. See shaded region in the figure. If the area of this region is 42π and the radii of the two smaller circles have a ratio of 2 : 3. What is the radius of the largest circle(x)?

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An arbelos is the region bordered by three mutually tangent circles with co-linear centers. See shaded region in the figure. If the area of this region is 42π and the radii of the two smaller circles have a ratio of 2 : 3. What is the radius of the largest circle(x)?




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