在实际教学中,我们经常利用圆的性质来构造辅助圆,进而转化成直线和辅助圆的公共点来解决问题.一、利用同弧所对的圆周角相等构造辅助圆来找点题1如图1,在■ABCD中,E是AD上一点,延长CE到点F,使∠FBC=∠DCE.(1)求证:∠D=∠F;(2)用直尺和圆规在AD上作出一点P,使△BPC∽△CDP(保留作图痕迹,不写作法). In practice teaching, we often use the nature of the circle to construct the auxiliary circle, and then turn it into a common point of the straight line and the auxiliary circle to solve the problem.First, we construct the auxiliary circle with the same circular angle to the same arc 1. In ABCD, E is the last point of AD, extend CE to point F, so that ∠FBC = ∠DCE. (1) Verify: ∠D = ∠F; (2) Make a point on AD with ruler and compasses P, △ BPC ∽ △ CDP (keep drawing traces, not writing method).