一个优美几何难题征解
如图，五边形A，B，C，D，E既外接于圆，又内切于圆。<br />将五切点隔位相连，如此得到五个交点A″，B″，C″，D″，E″．<br />证明：此五点共圆。<br /><img src="http://hiphotos.baidu.com/%C8%E7%B9%DB/pic/item/0ef21e00e5493e89e850cdf1.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt='Click here to open new window\nCTRL+Mouse wheel to zoom in/out';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor='hand'; this.alt='Click here to open new window\nCTRL+Mouse wheel to zoom in/out';}" onclick="if(!this.resized) {return true;} else {window.open(this.src);}" onmousewheel="return imgzoom(this);" alt="" /><br /> <br />我做的一个推广： <br /> <br /> <br />定义 双心n边形：若n边形即存在外接圆，又存在内切圆，则称其为双心n边形． <br /> <br />双心n边形定理:双心n边形的n个切点隔位相连，所得n个交点共圆．<br /> <br />如图，即是n=6的情形．<br /> <br /><img src="http://hiphotos.baidu.com/%C8%E7%B9%DB/pic/item/9cdb11128447c7c0c2fd78f1.jpg" border="0" onload="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.alt='Click here to open new window\nCTRL+Mouse wheel to zoom in/out';}" onmouseover="if(this.width>screen.width*0.7) {this.resized=true; this.width=screen.width*0.7; this.style.cursor='hand'; this.alt='Click here to open new window\nCTRL+Mouse wheel to zoom in/out';}" onclick="if(!this.resized) {return true;} else {window.open(this.src);}" onmousewheel="return imgzoom(this);" alt="" /><br /> <br />老子曰：道生一，一生二，二生三．此之谓也！<br />诗曰：两心之外又一心，试问天下谁能解！<br /> <br />说明，一个双心n边形关乎两圆，即已有两个圆心，切点相连又引出第三个圆，即又生其心．<br>页:
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