人教版高中数学选修4-4第26页习题2.1第3题是:已知:M是正三角形ABC的外接圆上的一点,求证:|MA|~2+|MB|~2+|MC|~2为定值.笔者在研究此题的过程中,得到了下面一个有趣的推广命题.命题△ABC是椭圆(或圆)C:x~2/a~2+y~2/b~2=1(a>0,b>0)的内接三角形,且△ABC的重心是坐标原点O,M是坐标平面内的任意一点,则|MA|~2+|MB|~2+|MC|~2-3|OM|~2为 Pertinence High School Mathematics Elective 4-4 Page 26 Exercises 2.1 The third question is: It is known that M is a point on the circumcircle of an equilateral triangle ABC, verifying | MA | ~ 2 + | MB | ~ 2 + | MC | ~ 2 for the value of the author in the process of studying this question, got the following an interesting promotional proposition △ Proposition △ ABC is an ellipse (or circle) C: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> 0, b> 0), and the center of gravity of △ ABC is the coordinate origin O, where M is any point in the coordinate plane, then | MA | ~ 2 + | MB | ~ 2 + | MC | ~ 2-3 | OM | ~ 2 is