拿破仑将军是法国赫赫有名的皇帝,他不仅是著名的政治家,军事家,而且是一名有相当造诣的数学爱好者,他曾经提出这样一个问题.若在任意三角形BC的外侧作三个等边三角形△CAB′、△CAB′△ABC′,(如图所示),则它们的中心能构成一个正三角形.(此三角形被称为拿破仑三角形)你能证明这个问题吗? General Napoleon, the eminent French emperor, was not only a prominent politician and military strategist, but also a well-accomplished math enthusiast who once asked the question of whether to make three, etc., on the outside of an arbitrary triangle BC Triangles △ CAB ’, △ CAB’ △ ABC ’, (as shown), then their center can form a triangle (this triangle is called Napoleon triangle) Can you prove this problem?