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对于在已知直线上找点与已知点构成定角的问题,如果能根据题设和结论,构造出符合题意特征的辅助圆,即把题目中的固定角转化为圆周角问题,就能使问题得以顺利解决,这种方法不但能较好的达到解题的目的,还有利于培养学生分析问题的能力.请看下面的两个例题:例1如图1,B是线段AC的中点,过点C的直线l与AC成60°的角,在直线l上取一点P,使得∠APB=30°,则满足条件的点P的个数是().
For the problem of finding a fixed angle with a known point on a known straight line, if the auxiliary circle that meets the inscribed features can be constructed according to the theme and the conclusion, that is, the fixed angle in the title is converted into a circular angle problem Can solve the problem smoothly, this method can not only achieve the purpose of solving the problem well, but also help students to analyze the ability of the problem.Please see the following two examples: Example 1 As shown in Figure 1, B is the line AC Midpoint, point C and a straight line l AC angle of 60 °, taking a point P on the straight line l, so that ∠ APB = 30 °, then the number of points to meet the condition is ().