10. A square is split into nine identical squares, each with sides of length one unit. Circles are inscribed in two of these squares, as shown. What is the shortest distance between the two circles?
A $2 \sqrt{2}-1$
B $\sqrt{2}+1$
C $2 \sqrt{2}$
D 2
E 3
10. A Each square has side-length 1 unit, so by Pythagoras' Theorem the diagonals have length $\sqrt{1^{2}+1^{2}}=\sqrt{2}$. The distance between the two circles consists of a whole diagonal and two part diagonals (from the corner of a square to the circle). This is the same as the length of two whole diagonals, minus a diameter, that is $2 \sqrt{2}-1$.