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2012年陕西省中考数学试题第25题,不但题型新颖,而且解题方法有所创新,对于开拓学生知识视野,促进思维的角度,丰富解题策略有积极的推动作用.原题是:如图,正三角形ABC的边长为3+3~(1/2).(1)如图①,正方形EFPN的顶点E、F在边AB上,顶点N在边AC上,在正三角形ABC及其内部,以A为位似中心,作正方形EFPN的位似正方形E′F′P′N′,且使正方形E′F’P’N′的面积最大(不要求写出作法).(2)求(1)中作出的正方形E′F’P’N′的边长;(3)如图②,在正三角形ABC中放入正方形DEMN
In 2012, the 25th exam of the entrance exam questions in Shaanxi Province not only possesses novel questions but also has some innovative solutions. It has a positive impetus to enrich the questions-solving strategies in terms of exploring students’ horizons and promoting thinking. (1) As shown in Fig. 1, the vertices E, F of the square EFPN are on the side AB, the vertices N are on the side AC, and the triangle ABC on the side of the equilateral triangle ABC and In its interior, a bit-like square E’F’P’N ’for a square EFPN with A as a bit centered, and square E’F’P’N’ is maximized (no writing is required.) (2 ) Find the side of the square E’F’P’N ’made in (1); (3) Insert the square DEMN