Cho tam giác ABC có các đường cao BD và CE. Chứng minh bốn điểm B, E, D, C cùng nằm trên một đường tròn. Chỉ rõ tâm và bán kính của đường tròn đó.
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![](https://rs.olm.vn/images/avt/0.png?1311)
Đường tròn (O) ngoại tiếp ∆ABC với BC là đường kính. Gọi O là trung điểm của BC. Chứng minh B,C,D,E nằm trên O ; B C 2
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác BEDC có
\(\widehat{BEC}=\widehat{BDC}=90^0\)
nên BEDC là tứ giác nội tiếp
=>B,E,D,C cùng thuộc 1 đường tròn
b: Vì \(\widehat{BEC}=\widehat{BDC}=90^0\)
nên B,E,D,C cùng thuộc đường tròn đường kính BC
tâm là trung điểm I của BC
bán kính là BC/2
c: Xét ΔABC có
BD,CE là đường cao
BD cắt CE tại H
Do đó: H là trực tâm của ΔABC
=>AH\(\perp\)BC(1)
ΔABC cân tại A
mà AI là đường trung tuyến
nên AI\(\perp\)BC(2)
Từ (1),(2) suy ra A,H,I thẳng hàng
ΔABC đều
mà BD,CE là các đường cao
nên BD,CE là các đường trung tuyến
=>D,E lần lượt là trung điểm của AC,AB
Xét ΔABC có
BD,CE là các đường trung tuyến
BD cắt CE tại H
Do đó; H là trọng tâm của ΔABC
mà I là trung điểm của BC
nên \(AH=\dfrac{2}{3}AI\) và \(IH=\dfrac{1}{3}IA\)
ΔAIB vuông tại I
=>\(AB^2=AI^2+IB^2\)
=>\(AI^2=2^2-1^2=3\)
=>\(AI=\sqrt{3}\left(cm\right)\)
\(HI=\dfrac{1}{3}HA=\dfrac{1}{3}\sqrt{3}< \dfrac{1}{3}\cdot3=IB=R\)
=>H nằm trong (I)
\(IA=\sqrt{3}>1=IB=R\)
=>A nằm ngoài (I)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét tứ giác BEDC có
\(\widehat{BEC}=\widehat{BDC}=90^0\)
Do đó: BEDC là tứ giác nội tiếp
Tâm là trung điểm của BC
Bán kính là \(\dfrac{BC}{2}=\dfrac{a}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Gọi G là trung điểm của BC
Ta có: ΔDBC vuông tại D(BD\(\perp\)AC tại D)
mà DG là đường trung tuyến ứng với cạnh huyền BC(G là trung điểm của BC)
nên \(DG=\dfrac{BC}{2}\)(Định lí 1 về áp dụng hình chữ nhật vào tam giác vuông)(1)
Ta có: ΔEBC vuông tại E(CE\(\perp\)AB)
mà EG là đường trung tuyến ứng với cạnh huyền BC(G là trung điểm của BC)
nên \(EG=\dfrac{BC}{2}\)(Định lí 1 về áp dụng hình chữ nhật vào tam giác vuông)(2)
Ta có: G là trung điểm của BC(gt)
nên \(BG=CG=\dfrac{BC}{2}\)(3)
Từ (1), (2) và (3) suy ra GB=GC=GE=GD
hay B,C,D,E cùng nằm trên một đường tròn(đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
- có \(\Delta BDC\)vuông tại D
nên D thuộc đường tròn đường kính BC ( 1)
có \(\Delta BEC\)vuông tại E
nên E thuộc đường tròn đường kính BC (2)
từ (1) và (2) suy ra đpcm
- gọi O là trung điểm của BC
có AO vuông góc với BC
dễ thấy OE > OH
nên H nằm trong đường tròn đường kính BC
dễ cm OA > OB
ên A nằm ngoài đường tròn đường kính BC
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Gọi O là trung điểm của AH thì OE = OA = OH = OD
b, HS tự làm
Lời giải:
Vì $\widehat{BEC}=\widehat{BDC}=90^0$ và cùng nhìn cạnh $BC$ nên $BEDC$ là tứ giác nội tiếp.
$\Rightarrow B,E,D,C$ cùng nằm trên một đường tròn.
Gọi $M$ là trung điểm $BC$.
Tam giác vuông $BEC$ có trung tuyến $EM$ tương với với cạnh huyền $BC$ nên $EM=\frac{BC}{2}=BM=CM$
Tương tự với tam giác $BDC$ vuông tại $D$ thì $DM=\frac{BC}{2}=BM=CM$
Do đó:
$EM=BM=CM=DM$ nên tâm đường tròn ngoại tiếp tứ giác $BEDC$ là điểm $M$- trung điểm $BC$
Hình vẽ:
![](data:image/png;base64,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)