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![](https://rs.olm.vn/images/avt/0.png?1311)
a: Gọi AH là tiếp tuyến chung của hai đường tròn (O) và (O'), H∈MN
Xét (O) có
HM,HA là các tiếp tuyến
Do đó: HM=HA và HO là phân giác của góc MHA
Xét (O') có
HA,HN là các tiếp tuyến
Do đó: HA=HN và HO' là phân giác của góc AHN
Ta có: HM=HA
HN=HA
Do đó: HM=HN
=>H là trung điểm của MN
Xét ΔAMN có
AH là đường trung tuyến
\(AH=\dfrac{MN}{2}\)
Do đó: ΔAMN vuông tại A
=>\(\widehat{MAN}=90^0\)
b: HO là phân giác của góc MHA
=>\(\widehat{MHA}=2\cdot\widehat{OHA}\)
HO' là phân giác của góc AHN
=>\(\widehat{AHN}=2\cdot\widehat{AHO'}\)
Ta có: \(\widehat{MHA}+\widehat{NHA}=180^0\)(hai góc kề bù)
=>\(2\cdot\left(\widehat{OHA}+\widehat{O'AH}\right)=180^0\)
=>\(2\cdot\widehat{OHO'}=180^0\)
=>\(\widehat{OHO'}=90^0\)
Xét ΔHO'O vuông tại H có HA là đường cao
nên \(HA^2=OA\cdot O'A\)
=>\(HA^2=9\cdot4=36\)
=>\(HA=\sqrt{36}=6\left(cm\right)\)
MN=2*HA
=>MN=2*6=12(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
ΔOIO' vuông tại A có IA là đường cao nên theo hệ thức giữa cạnh và đường cao ta có:
IA2 = AO.AO' = 9.4 = 36
=> IA = 6 (cm)
Vậy BC = 2.IA = 2.6 = 12 (cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Theo tính chất hai tiếp tuyến cắt nhau ta được IA = IB, IA = IC .
Tam giác ABC có đường trung tuyến \(AI=\frac{1}{2}BC\)nên là tam giác vuông
Vậy \(\widehat{BAC}=90^o\left(đpcm\right)\)
b) Theo tính chất hai tiếp tuyến cắt nhau ta có IO, IO' là các tia phân giác của hai góc kề bù AIB, AIC nên :
\(\widehat{OIO'}=\widehat{OIA}+\widehat{O'IA}=\frac{1}{2}\widehat{AIB}+\frac{1}{2}\widehat{AIC}=\frac{1}{2}\left(\widehat{AIB}+\widehat{AIC}\right)\)
Vậy : \(\widehat{OIO'}=90^o\)
c) \(\Delta OIO'\) vuông tại A có IA là đường cao nên theo hệ thức giữa cạnh và đường cao ta có:
IA2 = AO.AO' = 9 . 4 = 36
=> IA = 6 ( cm )
Vậy BC = 2 . IA = 2 . 6 = 12 (cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Ta có:(O) và (O') tiếp xúc ngoài tại A
=>A nằm giữa O và O'
=>B,O,A,O',C thẳng hàng
=>BA và CA lần lượt là đường kính của (O) và (O')
Kẻ tiếp tuyến chung AI của (O) và (O'), I\(\in\)DE
Xét (O) có
ID,IA là các tiếp tuyến
Do đó: ID=IA
Xét (O') có
IA,IE là các tiếp tuyến
Do đó: IA=IE
Ta có: ID=IA
IA=IE
Do đó: ID=IE
=>I là trung điểm của DE
Xét ΔADE có
AI là đường trung tuyến
AI=1/2DE
Do đó: ΔADE vuông tại A
=>\(\widehat{DAE}=90^0\)
b: Xét (O) có
ΔADB nội tiếp
AB là đường kính
Do đó: ΔADB vuông tại D
=>AD\(\perp\)MB tại D
Xét (O') có
ΔAEC nội tiếp
AC là đường kính
Do đó: ΔAEC vuông tại E
=>AE\(\perp\)MC tại E
Xét tứ giác MDAE có \(\widehat{MDA}=\widehat{MEA}=\widehat{DAE}=90^0\)
nên MDAE là hình chữ nhật
c: ta có: MDAE là hình chữ nhật
=>MA cắt DE tại trung điểm của mỗi đường
mà I là trung điểm của DE
nên I là trung điểm của MA
=>MA\(\perp\)BC tại A
=>MA là tiếp tuyến chung của (O) và (O')
Lời giải:
$(O), (O')$ tiếp xúc ngoài tại $A$ thì $O,A,O'$ thẳng hàng.
$OM\perp MN, O'N\perp MN$ (do $MN$ là ttc)
$\Rightarrow MNO'O$ là hình thang
$\Rightarrow \widehat{NO'A}+\widehat{MOA}=180^0$ (2 góc trong cùng phía).
Lại có:
Theo tính chất tiếp tuyến, góc thì:
$\widehat{AMN}= \frac{1}{2}\widehat{MOA}$
$\widehat{ANM}=\frac{1}{2}\widehat{NO'A}$
$\Rightarrow \widehat{AMN}+\widehat{ANM}=\frac{1}{2}(\widehat{MOA}+\widehat{NO'A})$
$=\frac{1}{2}.180^0=90^0$
$\Rightarrow \widehat{MAN}=90^0$
b. Từ $A$ kẻ tiếp tuyến $AT$ chung của $(O), (O')$
Theo tính chất 2 tt cắt nhau thì:
$AT=MT=TN$
$\Rightarrow MN=MT+TN= 2AT$
Cũng theo tính chất 2 tiếp tuyến cắt nhau thì $TO, TO'$ lần lượt là phân giác $\widehat{MTA}, \widehat{NTA}$
Mà $\widehat{MTA}+\widehat{NTA}=180^0$ nên $TO\perp TO'$
Tam giác $TOO'$ vuông có đường cao $TA$, áp dụng HTL:
$TA^2=OA.O'A=9.4=36$
$\Rightarrow TA=6$
$MN=2TA=2.6=12$ (cm)
Hình vẽ:
![](data:image/png;base64,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)