We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.

当三个质量ara位于等边三角形的顶点时，我们研究了五体问题中中心配置的凸性和对称性，我们称之为拉格朗日加上两个中心配置。首先，我们证明三角形顶点之外的两个物体不能放在某些直线上。接下来，我们在 Dziobek 的意义上给出了这种配置的几何特征，并描述了可以放置两个剩余物体的允许区域。此外，我们证明任何拉格朗日加上两个中心配置都是凹的。最后，我们用数值显示了五体问题的非对称中心配置的存在。