qjchen 发表于 2007-10-4 10:04:00

几何作图题41，已知内切圆，过圆心三射线，求做三角形

<p>几何作图题41，已知内切圆，过圆心三射线，求做三角形</p><p>：），不好意思，看到这道趣题，还是忍不住放上来，解法颇有趣</p><p>难度系数：4.0/5</p><p></p>

highflybir 发表于 2007-10-4 16:55:00

Andyhon 发表于 2007-10-4 17:40:00

本帖最后由 作者 于 2007-10-4 17:42:59 编辑 <br /><br /> <div><font face="細明體"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><strong><font face="Verdana" color="#da2549">highflybir</font></strong> 老师解得妙 </p><hr/><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><font face="細明體">&nbsp;关系式解法</font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">∠P=∠a+∠b+2∠c<br/>∠Q=∠b+∠c+2∠a<br/>∠R=∠c+∠a+2∠b<br/></p><hr/>∠P+∠a+∠b=∠Q+∠b+∠c=∠R+∠c+∠a</font><font face="新細明體"><br/>&nbsp;&nbsp;</font><p></p></div><div><font face="細明體">∠P-∠Q=∠a-∠c<br/>∠Q-∠R=∠b-∠a<br/>∠R-∠P=∠c-∠b</font></div><div><font face="細明體"></font>&nbsp;</div><div><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">△<font face="Times New Roman"><br/>&nbsp;&nbsp;&nbsp;</font><font face="新細明體">AoB 中 </font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 新細明體;">∠P+∠a+∠b=180°<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">&nbsp;</p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">&nbsp;</p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">&nbsp;</p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 新細明體;">∠a+∠b = 180°-∠P</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;">∠<font face="細明體">b-</font>∠<font face="細明體">a=</font>∠</span><font face="細明體">Q-</font>∠<font face="細明體">R</font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><font face="細明體">2<span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;">∠<font face="細明體">b=</font><font face="新細明體">180°-∠P+∠Q-∠R</font></span></span></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;">∠CBA<font face="細明體">=</font><font face="新細明體">180°+∠Q-∠R-∠P</font></span></span></font></span></span></span></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"></font></span></span></span></font></span>&nbsp;</p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;">∠P,∠Q,∠R 为已知 ; <font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><font face="細明體"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;"><span style="FONT-FAMILY: 新細明體;">∠CBA 可求</span></span></font></span></span></span></font></span></span></span></font></span></span></span></font></span></p></div>

qjchen 发表于 2007-10-5 09:12:00

<p>：）谢谢Highflybird兄的精彩做法和Andyhon兄的详细讲解。</p><p>Highflybird兄的做法比书上要简单，此下还是附上书上做法：）</p><p>&nbsp;</p>
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