Problem #130

Consider the solid bounded by the three right circular cylinders x2 + y2 = 2a2 (greenish-yellow), x2 + z2 = 2a2 (red), and y2 + z2 = 2a2 (blue) shown in the figure below. An ant wants to follow the shortest path along the surface from the point (a, a, 0) to the point (0, a, a). What is the length of this path?

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