# 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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