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问题已知三村庄A、B、C构成了如图1所示的△ABC(其中∠A、∠B、∠C均小于120°),现选取一点P打水井,使从水井P到三村庄A、B、C所铺设的输水管总长度最小,求输水管总长度的最小值.分析本题是一道关于最值的应用问题,题目给的信息量较少,不少学生无从下手解决问题,如果我们了解托勒密定理,并熟悉其应用,就给这类题型解答带来方便.托勒密定理如图2若四边形ABCD的
Problem It is known that three villages A, B, and C form △ ABC (where ∠A, ∠B and ∠C are both less than 120 °) as shown in Fig.1. Now choose a point P to fill the well, The total length of the water pipe laid by A, B and C is the minimum, and the minimum total length of the water pipe is required for the analysis. This analysis is a question about the application of the most value. There is less information for the topic, and many students have no solution to the problem. If we understand the Ptolemy theorem, and familiar with its application, give the answer to such questions to bring convenience. Ptolemy theorem shown in Figure 2 If the quadrilateral ABCD