Can anyone explain the geometry of the moorish or horseshoe arch?

Answer 1

Based on images
http://www.fotosearch.com/photos-images/moorish-arch.html
and definitions
a moorish arch is nothing more than a semicircular arch that flows smoothly into a vertical support. In other words, it has no transition or foot to rest on. As a semicircular arch it requires external bracing because such an arch tends to force its feet apart, doing a poor job of converting the thrust of the weight to the sides of the arch.