Abstract: Four properties of circum-circles for Delaunay triangulation of point set generated from uniformly partitioning the boundary of 2D domain are presented.These four properties predict the relationship between Delaunay triangulation and geometrical features of 2D domain.Based on these properties,the method to automatically recognize geometrical features and adaptively generate meshes is built. The method is applied successfully to2D finite element adaptive mesh generation,taking into consideration geometrical features along with some mechanical features.