《中学生数学》2010年第9期(月下)“智慧窗”第5题“巧作圆,妙求值”为:如图1,在△ABC中,AB=AC,BA⊥AP,AP交BC边于点P,求(BP·BC)/AB2的值.参考答案中的作法是:如图1,作△ABC的外接圆,然后应用圆的有关知识及相似三角形,使问题获解.这种方法不仅解题过程较复杂,而且不容易想到!下面给出另一种更为简洁且容易想到的方法: “Middle School Mathematics” 2010 the ninth period (under the moon) “Wisdom window ” the fifth question “clever for the circle, wonderful seeking value ” as follows: As shown in Figure 1, in ABC, AB = AC, BA AP, AP intersection BC edge at point P, (BP · BC) / AB2 value. The reference answer approach is: as shown in Figure 1, △ ABC circumcircle, and then use the circle of knowledge and similar triangles, so The problem is solved.This method not only the problem-solving process is more complex, and not easy to think! Here is another more concise and easy to think of the method: