题目
题型:不详难度:来源:
当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-83241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-72135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-51656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
探究证明:
如图所示,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-54048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-75752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-76313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-52651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-62978.png)
(1)分别用
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-41206.png)
(2)探求OC与CD表达式之间存在的关系(用含a,b的式子表示).
归纳结论:
根据上面的观察计算、探究证明,你能得出
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
实践应用:
要制作面积为4平方米的长方形镜框,直接利用探究得出的结论,求出镜框周长的最小值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-83241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-72135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-51656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
探究证明:(1)OC=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-87492.png)
(2)当a=b时,OC=CD,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
结论归纳:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212143-97416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
实践应用:周长最小为4米.
解析
试题分析:观察计算:把
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-83241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-72135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-51656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
探究证明:(1)由于OC是直径AB的一半,则OC易得.通过证明△ACD∽△CBD,可求CD;
(2)分a=b,a≠b讨论可得出
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
实践应用:通过前面的结论长方形为正方形时,周长最小.
试题解析:观察计算:当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-83241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-72135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-51656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
探究证明:
(1)∵AB=AD+BD=2OC,
∴OC=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
∵AB为⊙O直径,
∴∠ACB=90°.
∵∠A+∠ACD=90°,∠ACD+∠BCD=90°,
∴∠A=∠BCD.
∴△ACD∽△CBD.
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212143-72865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212142-87492.png)
(2)当a=b时,OC=CD,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
a≠b时,OC>CD,
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
结论归纳:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-36074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212143-97416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212141-75917.png)
实践应用
设长方形一边长为x米,则另一边长为
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212143-22580.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212143-11502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212144-95688.png)
此时四边形为正方形时,周长最小为4米.
核心考点
试题【观察计算:当,时,与的大小关系是_________________.当,时,与的大小关系是_________________.探究证明:如图所示,为圆O的内接三】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212127-95313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-57291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-31321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212128-57553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-49274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-68517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212129-28641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-34535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-10703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-88579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212130-21562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-38893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-91635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-71841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212131-42734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212132-52592.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212132-87502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-70294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-31490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212119-95573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212120-20488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212114-37012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102212114-64143.jpg)