尺规作图：在一个圆里，画一个正五边形，要求五个顶点在圆的曲线上。 如何用尺规作图的方法做一个正五边形
\u5982\u4f55\u5728\u4e00\u4e2a\u5706\u4e2d\u7528\u5c3a\u89c4\u4f5c\u56fe\u82b1\u4e00\u4e2a\u6b63\u4e94\u8fb9\u5f62\u5706\u5185\u63a5\u6b63\u4e94\u8fb9\u5f62\u7684\u753b\u6cd5\u5982\u4e0b\uff1a \uff081\uff09\u4ee5O\u4e3a\u5706\u5fc3\uff0c\u5b9a\u957fR\u4e3a\u534a\u5f84\u753b\u5706\uff0c\u5e76\u4f5c\u4e92\u76f8\u5782\u76f4\u7684\u76f4\u5f84MN\u548c AP. \uff082\uff09\u5e73\u5206\u534a\u5f84ON\uff0c\u5f97OK=KN. \uff083\uff09\u4ee5 K\u4e3a\u5706\u5fc3\uff0cKA\u4e3a\u534a\u5f84\u753b\u5f27\u4e0e OM\u4ea4\u4e8e H\uff0c AH\u5373\u4e3a\u6b63\u4e94\u8fb9\u5f62\u7684\u8fb9\u957f. \uff084\uff09\u4ee5AH\u4e3a\u5f26\u957f\uff0c\u5728\u5706\u5468\u4e0a\u622a\u5f97A\u3001B\u3001C\u3001D\u3001E\u5404\u70b9\uff0c\u987a\u6b21\u8fde\u63a5\u8fd9\u4e9b\u70b9\u5373\u5f97\u6b63\u4e94\u8fb9\u5f62.
\u3000\u3000\u5e38\u89c4\u753b\u6cd5
\u3000\u3000(1)\u5df2\u77e5\u8fb9\u957f\u4f5c\u6b63\u4e94\u8fb9\u5f62\u7684\u8fd1\u4f3c\u753b\u6cd5
\u3000\u3000\u2460\u4f5c\u7ebf\u6bb5AB\u7b49\u4e8e\u5b9a\u957fl,\u5e76\u5206\u522b\u4ee5A,B\u4e3a\u5706\u5fc3,\u5df2\u77e5\u957fl\u4e3a\u534a\u5f84\u753b\u5f27\u4e0eAB\u7684\u4e2d\u5782\u7ebf\u4ea4\u4e8eK\u3002
\u3000\u3000\u2461\u53d6AB\u76842/3\u957f\u5ea6\uff0c\u6cbf\u7740\u4e2d\u5782\u7ebf\u5411\u4e0a\u53d6C\u70b9\uff0c\u4f7fCK=2/3AB\u3002
\u3000\u3000\u2462\u4ee5\u70b9C\u4e3a\u5706\u5fc3\uff0c\u5df2\u77e5\u8fb9\u957fAB\u4e3a\u534a\u5f84\u753b\u5f27\uff0c\u5206\u522b\u4e0e\u524d\u4e24\u5f27\u76f8\u4ea4\u4e8eM\uff0cN\u3002
\u3000\u3000\u2463\u987a\u6b21\u8fde\u63a5A\uff0cB\uff0cN\uff0cC\uff0cM\u5404\u70b9\u5373\u8fd1\u4f3c\u4f5c\u5f97\u6240\u8981\u6c42\u7684\u6b63\u4e94\u8fb9\u5f62\u3002
\u3000\u3000(2)\u6c11\u95f4\u53e3\u8bc0\u753b\u6b63\u4e94\u8fb9\u5f62
\u3000\u3000\u53e3\u8bc0\u4ecb\u7ecd\uff1a\u201c\u4e5d\u4e94\u9876\u4e94\u4e5d,\u516b\u4e94\u4e24\u8fb9\u5206\u201d\u3002
\u3000\u3000\u753b\u6cd5:
\u3000\u3000\u2460\u753b\u7ebf\u6bb5AB=20mm\u3002
\u3000\u3000\u2461\u4f5c\u7ebf\u6bb5AB\u7684\u5782\u76f4\u5e73\u5206\u7ebfl\uff0c\u5782\u8db3\u4e3aG\u3002
\u3000\u3000\u2462\u5728l\u4e0a\u8fde\u7eed\u622a\u53d6GH\uff0cHD\uff0c\u4f7f GH=9.5/5*10mm=19mm\uff0cHD=5.9/5*10mm=11.8mm\u3002
\u3000\u3000\u2463\u8fc7H\u4f5cEC\u22a5HG,\u5728EC\u4e0a\u622a\u53d6HE=HC=8/5*10mm=16mm\u3002
\u3000\u3000\u2464\u8fde\u7ed3DE\uff0cEA\uff0cAB\uff0cBC\uff0cCD\u3002
\u3000\u3000\u4e94\u8fb9\u5f62ABCDE\u5c31\u662f\u8fb9\u957f\u4e3a20mm\u7684\u8fd1\u4f3c\u6b63\u4e94\u8fb9\u5f62\u3002
\u3000\u3000\u5c3a\u89c4\u4f5c\u56fe\u753b\u6cd5
\u3000\u3000\u7406\u8bba\u4f9d\u636e\uff1acos36\u00b0=(1+\u221a5)/4
\u3000\u3000\u6b63\u4e94\u8fb9\u5f62 - \u51e0\u4f55\u753b\u677f
\u3000\u30001. \u5728\u5e73\u9762\u5185\u4f5c\u4e00\u5706\uff0c\u5706\u5fc3\u4e3aO\uff1b
\u3000\u30002. \u5728\u5706O\u4e0a\u53d6\u4e00\u70b9A\uff0c\u8fde\u63a5AO\u5e76\u5ef6\u957f\u4ea4\u5706O\u4e8e\u53e6\u4e00\u70b9B\uff1b\u3010\u5047\u4ee4|AB|=4\u3011
\u3000\u30003. \u8fc7\u70b9O\u4f5cCD\u22a5AB\uff0c\u4ea4\u5706O\u4e8eC\u3001D\u4e24\u70b9\uff1b\u3010\u6b64\u65f6|CD|=4\u3011
\u3000\u30004. \u4f5cOB\u5782\u76f4\u5e73\u5206\u7ebfMN\uff0c\u4ea4OB\u4e8eE\u70b9\uff0c\u4ea4\u5706O\u4e8eM\uff0cN\u3010\u6b64\u65f6|OE|=|BE|=1\u3011
\u3000\u30005. \u4ee5\u70b9E\u4e3a\u5706\u5fc3\uff0cEC\u957f\u4e3a\u534a\u5f84\u4f5c\u5f27\uff0c\u4ea4BO\u5ef6\u957f\u7ebf\u4e8e\u70b9F\uff1b
\u3000\u3000\u3010\u6b64\u65f6|EC|=|EF|=\u221a5\u3011
\u3000\u30006. \u4ee5\u70b9B\u4e3a\u5706\u5fc3\uff0cBF\u957f\u4e3a\u534a\u5f84\u4f5c\u5f27\uff0c\u4ea4\u5706O\u5206\u522b\u4e8eG\u3001H\u4e24\u70b9\uff1b\u3010\u6b64\u65f6|BF|=|EF|+|BE|=1+\u221a5\u3011
\u3000\u3000\u3010\u6b64\u65f6\u53ef\u77e5cos\u2220ABG=(|EF|+|BE|)/|AB|=(1+\u221a5)/4=cos36\u00b0\u3011
\u3000\u3000\u3010\u800c\u2220AOG=2\u2220ABG=72\u00b0=360\u00b0/5(\u76f4\u5f84\u6240\u5bf9\u7684\u5706\u5468\u89d2)\u3011
\u3000\u3000\u3010\u6b64\u65f6\u4fbf\u5f97\u5230\u4e86\u5706\u5468\u4e0a\u7684\u4e94\u7b49\u5206\u70b9\u7684\u5176\u4e2d\u4e24\u4e2a\u3002\u3002\u3002\u3002\u3002\u3011
\u3000\u30007. \u4ee5\u70b9G\u4e3a\u5706\u5fc3\uff0cGA\u957f\u4e3a\u534a\u5f84\u4f5c\u5f27\uff0c\u4ea4\u5706O\u4e8eP\u70b9\uff1b
\u3000\u30008. \u4ee5\u70b9H\u4e3a\u5706\u5fc3\uff0cHA\u957f\u4e3a\u534a\u5f84\u4f5c\u5f27\uff0c\u4ea4\u5706O\u4e8eQ\u70b9\uff1b
\u3000\u30009. \u8fde\u63a5AG\u3001GP\u3001PQ\u3001QH\u3001HA,\u5219\u4e94\u8fb9\u5f62AGPQH\u4e3a\u6b63\u4e94\u8fb9\u5f62\u3002
步骤如下:
1.以O为圆心,以R为半径作圆.
2.过圆心O作直线交圆O于A,B两点.
3.作线段AB的中垂线与圆O交与M,N两点.
4.作线段AO的中垂线EF交AB与点G.
5.以G为圆心,以MG为半径画弧,交OB于点H.
6.综上,MH即为所求正五边形的边长,以MH为半径在圆上依次截取5个点.那么这5个点即为正五角星的5个顶点(且这么说吧).
7.交叉连接这5个点即可得正五角星.作毕.
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