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我们在学习《圆》这一章时,常会见到一些已知图形是半圆的几何题.如果我们仅仅在半圆中探求解题思路,那么往往会跃蹰不前,知难而返;如果我们把半圆补成整圆,那么就可利用圆的对称性或其他性质,发现隐含在另半圆中的某些条件,从而找到解题捷径,兹举数例,以示一斑, 例1 如图1,AB是半圆的百径,C、D是AB上两点,M、P、N是半圆上三点,且∠ACM=∠BCP,∠ADP=∠BDN,若AM、BN的度数分别是20°和60°,求∠P的度数.
When we study the chapter “Circle,” we often see some known geometric shapes that are semi-circular. If we only explore the problem in the semi-circle, we will often be leaping forward and we will return; if we To make up a semicircle, you can use the symmetry or other properties of the circle to find out the conditions that are implicit in the other semicircle, so as to find the shortest way to solve the problem, here are a few examples to illustrate. Example 1 1,AB is a semicircle of hundred paths, C, D are two points on AB, M, P, N are three points on a semicircle, and ∠ACM=∠BCP, ∠ADP=∠BDN, if the degrees of AM and BN are 20° and 60°, find the degree of P.