I think geometry will help

Geometry Level 5

Let \(A\) be the point \((8,6)\) and \(D\) be the point \((6,4)\). If the length of the shortest path \(ABCD\) can be expressed as \(\sqrt{a} + b \), where \(B\) is the point \((x,3)\) and \(C\) is a point \((x,0)\). This path consists of three connected segments, with the middle one vertical.

Find the value of \(a - b\).

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