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对于一个正n(n≥5)边形A_1A_2…A_n,过它的一个顶点A_1连n-3条对角线,将这个正多边形分成n-2个三角形,本文给出有关这些三角形重心和垂心的两个性质.性质1设n-2个三角形的重心分别为W_1,W_2,…,W_(n-2),则这n-2个点共圆.这个圆的圆心M在正多边形的外接圆过A_1点的直径上,且圆心是直径的靠近A_1点的一个三等分点.图一和图二分别画出了n=8和n=9两种情形.
For a positive n (n≥5) edge A_1A_2...A_n, pass one of its vertices A_1 to n-3 diagonals, and divide this regular polygon into n-2 triangles. This paper gives information about the center of gravity and the center of gravity of these triangles. Two properties. The property 1 sets the center of gravity of the n-2 triangles to W_1, W_2,..., W_(n-2), then the n-2 points are co-circular. The circle’s center M is outside the regular polygon. Circle the diameter of the A_1 point, and the center of the circle is a three-divided point close to the A_1 point of the diameter. Figure 1 and Figure 2 respectively show two cases of n=8 and n=9.