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2013年全国高中数学联赛加试(A卷)的平面几何题,以简洁优美的图形、多维的思维视角,激发着考生的求解欲望.从不同的角度运用几何图形特征,建立相关量之间的联系,可以得到不同的几何证法;从不同的视角观察图形,利用正弦定理及三角形的面积关系,又可得到不同的三角方法.本文提供的7种证明方法,以不同的方式展现出了不一样的精彩;有的方法仅用到中学课本的知识,甚至只用到初中课本的知识,下面请大家欣赏.试题如图1,AB是圆ω的一条弦,P为AB上一点,E、F为线段AB上两点,满足AE=EF=FB.连结PE、PF并延长,与圆ω分别相交于点C、D.求证:EF·CD=AC·BD.
In 2013, the plane geometry problem of the A-level high school mathematics league plus test (A) is stimulated by the simple and graceful graphics and multidimensional thinking perspectives, and the geometrical features are used from different angles to establish the correlation between the relevant quantities Contact, you can get different geometric card law; from different perspectives to observe the graphics, the use of the sine and the triangle area relationship, but also to get a different triangle method.This paper provides seven kinds of proof methods, in different ways showed no The same wonderful; some methods only use the knowledge of high school textbooks, and even only use the knowledge of junior high school textbooks, please enjoy the following ... Test questions shown in Figure 1, AB is a chord of a circle ω, P is the last point AB, E, F for the two points on the line segment AB, to meet the AE = EF = FB. Link PE, PF and extended, and the intersection of ω, respectively, at points C, D. Confirmation: EF · CD = AC · BD.