A semicircular arch of radius a stands on level ground as shown in the figure. The arch is uniform in cross section and density, with total weight W. By symmetry, at the top of the arch, each of the two legs exerts only horizontal forces on the other; ideally, the stress at that point is uniform compression over the cross section of the arch. What are the vertical and horizontal force components which must be supplied at the base of each leg to support the arch?

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