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In relation to this geometric construction:

construction

where D is the center of both circles, if the inner radius (x = length of line segments DA and DE), the angle φ = ∠CAB, and the length Δg of line segment AB are given, what is the length Δx of line segment AC?

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@muad: The inner radius is non-zero, but if it were, then Δx—the length that I seek—would be equal to the given value Δg. I cannot assign a value to the inner radius, Δg, or φ because these are all given quantities. – Daniel Trebbien Sep 26 '10 at 15:19

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Consider the triangle DAB. You know two sides and an angle. The length of the third side is $x + \Delta x$.

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