Longest Distance

Geometry Level 4

In the image, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points \(W\), \(X\), \(Y\), and \(Z\) is a vertex of one of the small squares. Square \(ABCD\) can be constructed with sides passing through \(W\), \(X\), \(Y\), and \(Z\).

The maximum possible distance from \(A\) to \(P\) is closest to which of the following numbers?


Problem and Image Source: CEMC (Past Contests).
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