在文 [1 ]中 ,我们借助于向量得到了圆内接闭折线垂心的一个性质 .本文仍用这一方法 ,证明它的一个新的性质 .定理　设闭折线 A1A2 … An A1内接于⊙ ( O,R) ,其垂心为 H ,则有OH 2 =R2 ( n + 2 ∑1≤ ij≤ ncos∠ Ai OAj) 1证明　在闭折线 A1A2 … An A1所在平面内 ,以其外心 In [1], we obtain a property of the center of the circle in which the circle is closed by means of a vector. This article still uses this method to prove a new property of it. The theorem sets the closed polyline A1A2 ... An A1 inscribed in (O,R), whose vertical center is H, then OH 2 =R2 ( n + 2 ∑1≤ ij≤ ncos∠ Ai OAj) 1 Prove that in the plane of the closed line A1A2 ... An A1, with its outer heart