题目
题型:不详难度:来源:
DE⊥EB
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005912-22335.png)
(1)求证:AC是△BDE的外接圆的切线;
(2)若AD=6,AE=6
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005912-39828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005912-93938.png)
答案
解析
(Ⅰ)要证明AC是△BDE的外接圆的切线,故考虑取BD的中点O,只要证明OE⊥AC,结合∠C=90°,证明BC∥OE即可
(Ⅱ)设⊙O的半径为r,则在△AOE中,由OA2=OE2+AE2,可求r,代入可得OA,2OE,Rt△AOE中,可求∠A,∠AOE,进而可求∠CBE=∠OBE,在BCE中,通过EC与BE的关系可求
解:(1)取BD的中点O,连结OE
∵DE⊥EB
∴DB是△BED的外接圆的直径,
∴OE是⊙O的半径
∴BE平分∠ABC
∴∠ABE=∠EBC
∵OE=OB ∴∠ABE=∠DEO
∴∠DEO=∠EBC,∴EO∥BC
∵∠C=90º,∴∠AEO=90º ∴AC是⊙O的切线……….6分
(2)由(1)得:AE2=AD•AB
∴(6
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005912-39828.png)
∵EO∥BC,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005913-14350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005913-93749.png)
核心考点
试题【.(12分)如图,在Rt△ABC中,∠C=90º,BE平分∠ABC交AC于点E,点D在AB上,DE⊥EB(1)求证:AC是△BDE的外接圆的切线;(2)若AD=】;主要考察你对圆锥曲线性质探讨等知识点的理解。[详细]
举一反三
已知C点在圆O直径BE的延长线上,CA切圆O于A点,DC是
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005902-85005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005902-85304.png)
(1) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005902-52603.png)
(2) 若AB=AC,求AC:BC.
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005856-62727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005856-52693.jpg)
如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005850-44532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005851-19900.jpg)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005851-88481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005851-59537.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005851-72589.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005850-44532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005852-74776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005852-46313.png)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005844-85083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005844-85435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005844-68733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005844-68733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005844-71680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005845-79202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005845-65060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005845-14655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005845-76996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005846-71152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005846-14055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005846-56697.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005841-59972.png)