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Geometry Level 3

An infinite series of similar triangles converge to a point C . If \( \overline{AE} = 16 , \overline{ED} = 8 \) . Denote \(x\) as the sum of all the vertical segments: \( \overline{AE} + \overline{BD} + \ldots \)

Find the value of \(x\).

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