漳州中考数学第26题

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1、初中数学研究网·初中对话数学www.czsxyj.com张越初中数学·挑战2012数学中考2009年中考数学佳题赏析研究2009漳州中考数学第26题改编题推荐星级☆☆☆☆如图①，已知：△ABC的三个顶点的坐标分别为A(-1,0)、B(4,0)、C(0,-2),(1)求证∠ACB=90º;(2)△ABC内部能否截出面积最大的矩形DEFG（顶点D、E、F、G在△ABC各边上）？若能，求出在AB边上的矩形顶点的坐标；若不能，请说明理由．解答或提示〖关键词·综合题·勾股定理的逆定理·相似三角形·函数的应用·二次函数的最大值·位置讨论〗（1）依勾股定理的逆定理可证∠ACB=90

2、º．（2）能．分两种情况讨论如下:①当矩形两个顶点在AB上时，如图甲，设CO交GF于H．设GF=x,由△CGF∽△CAB,易求得,,===.∴当时,最大.此时,由△ADG∽△AOC,易得.∴D,E(2,0).②当矩形一个顶点(D)在AB上时，F与C重合，如图乙.初中数学研究网·初中对话数学www.czsxyj.com类似地,可求当DG=时,最大.此时,D.欢迎光临初中数学研究网www.czsxyj.com内部资料仅供参考9JWKffwvG#tYM*Jg&6a*CZ7H$dq8KqqfHVZFedswSyXTy#&QA9wkxFyeQ^!djs#XuyUP2kNXpRW

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