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几何极值问题是初中几何的一个难点,由于它涉及的知识点较多,学生思维起步较困难,所以许多学生认为它很神秘.其实初中课本就有一个(人教版初中几何第二册P89 例3): 如图1,要在河边修建一个水泵站,分别向张村、李庄送水.水泵站修在河边什么地方,可使所用的水管最短? 已知:直线a和a同侧两点A、B. 求作:点C,使C在直线a上,并且AC+CB最小.
Geometry extremum problem is a difficult point in junior high school geometry. Because it involves more knowledge points, students’ thinking is difficult to start, so many students think it is very mysterious. In fact, there is one in junior high school textbooks (Personal education junior high school geometry second volume P89 Example 3): As shown in Figure 1, a water pumping station is to be built beside the river to send water to Zhangcun and Lizhuang respectively. Where does the pump station be repaired at the riverside and the shortest water pipe can be used? Known: Straight lines a and a Side two points A, B. 求作: Point C, makes C on the straight line a, and AC+CB is the smallest.