A Four-Body Convex Central Configuration with Perpendicular Diagonals Is   Necessarily a Kite
  We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem. 
Montserrat Corbera, Josep M. Cors, Gareth E. Roberts
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