Avoid the Annoying Circular Objects

Geometry Level 3

You are currently located on point \((0,0)\) and you want to get on point \((54,18)\). However, there are some annoying circular objects in the way! They are defined by \[x^2+y^2-18x-18y+81=0\] \[x^2+y^2-90x-18y+2025=0\]

If you cannot walk through these annoying circular objects, then the shortest possible path possible to point \((54,18)\) can be expressed as \[a+b\sqrt{c}+d\pi\] for positive integers \(a,b,c,d\) with \(c\) square-free. What is \(a+b+c+d\)?

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