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一、问题提出题目在△ABC中,A,B,C的对边分别为a,b,c.O为△ABC所在平面内一点,若aOA+b OB+c OC=0,则点O为△ABC的内心.在高三复习中,很多同学问过上面这道题,想得到O为内心,需要论证它是△ABC内角平分线的交点,但根据题目中所给向量等式,实在不知该从哪入手,题中的这个等式究竟隐含了哪些信息呢?二、方法探寻联想相似问题,借鉴相应的解决办法,是攻克数学问题的有效策略,这让我们想到这样一道高考题.
First, the problem proposed in △ ABC, A, B, C on the opposite side were a, b, cO △ ABC where the plane point, if aOA + b OB + c OC = 0, then the point O is △ ABC In the third year of review, many students asked this question above, and wanted to get O as the heart. We need to demonstrate that it is the intersection point of the △ABC internal angle bisector, but according to the vector equation given in the title, I really don’t know where to start. What is the information implied by this equation in the question? Second, the method to explore the similarity problem of Lenovo and learn from the corresponding solutions is an effective strategy to overcome mathematical problems. This reminds us of such a college entrance examination question.