1) cho △ABC, đường cao BD, CE cắt nhau tại H
a) c/m: A, D, H, E cùng thuộc 1 đường tròn
b) c/m: B, D, E, C cùng thuộc 1 đường tròn
giúp mk vs ạ mk cần gấp
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a) Ta có AD là đường cao của △ABC (gt)
=> AD⊥BC =>
Tương tự ta có
Tứ giác CEHD có : => Tứ giác CEHD là tứ giác nội tiếp => 4 điểm C,H,D,E cùng thuộc 1 đường tròn
a: Xét tứ giác ADHE có
\(\widehat{AEH}+\widehat{ADH}=180^0\)
Do đó: ADHE là tứ giác nội tiếp
hay A,D,H,E cùng thuộc 1 đường tròn
b: Xét tứ giác BEDC có
\(\widehat{BEC}=\widehat{BDC}=90^0\)
Do đó: BEDC là tứ giác nội tiếp
hay B,E,D,C cùng thuộc 1 đường tròn
Tứ giác ADHE có \(\widehat{ADH}+\widehat{AEH}=90+90=180\) nên là tứ giác nội tiếp
Suy ra A,D,H,E thẳng hàng
Xét tứ giác ADHE có
\(\widehat{ADH}+\widehat{AEH}=180^0\)
Do đó: ADHE là tứ giác nội tiếp
a: Xét tứ giác BCDE có
\(\widehat{BEC}=\widehat{BDC}\left(=90^0\right)\)
Do đó: BCDE là tứ giác nội tiếp
hay B,C,D,E cùng thuộc 1 đường tròn
b: Xét (O) có
ΔAPC nội tiếp đường tròn
AC là đường kính
Do đó: ΔAPC vuông tại P
Xét (I) có
ΔAQB nội tiếp đường tròn
AB là đường kính
Do đó: ΔAQB vuông tại Q
Xét ΔAPC vuông tại P có PD là đường cao ứng với cạnh huyền AC
nên \(AP^2=AD\cdot AC\left(1\right)\)
Xét ΔAQB vuông tại Q có QE là đường cao ứng với cạnh huyền AB
nên \(AQ^2=AE\cdot AB\left(2\right)\)
Xét ΔADB vuông tại D và ΔAEC vuông tại E có
\(\widehat{EAC}\) chung
Do đó: ΔADB\(\sim\)ΔAEC
Suy ra: \(\dfrac{AD}{AE}=\dfrac{AB}{AC}\)
hay \(AB\cdot AE=AD\cdot AC\left(3\right)\)
Từ (1), (2) và (3) suy ra AP=AQ
hay ΔAPQ cân tại A
a: Xét tứ giác BEDC có
\(\widehat{BEC}=\widehat{BDC}=90^0\)
=>BEDC là tứ giác nội tiếp đường tròn đường kính BC
Tâm I là trung điểm của BC
b: Xét ΔADB vuông tại D và ΔAEC vuông tại E có
\(\widehat{DAB}\) chung
Do đó: ΔADB đồng dạng với ΔAEC
=>\(\dfrac{AD}{AE}=\dfrac{AB}{AC}\)
=>\(AD\cdot AC=AB\cdot AE\)
c: Xét tứ giác BHCK có
I là trung điểm chung của BC và HK
nên BHCK là hình bình hành
=>BH//CK và BK//CH
=>\(CK\perp AC;AB\perp BK\)
Xét tứ giác ABKC có
\(\widehat{ABK}+\widehat{ACK}=90^0+90^0=180^0\)
=>ABKC là tứ giác nội tiếp đường tròn đường kính AK
=>ΔABC nội tiếp đường tròn đường kính AK
=>A,O,K thẳng hàng và O là trung điểm của AK
d: XétΔKAH có
I,O lần lượt là trung điểm của KH,KA
=>IO là đường trung bình
=>AH=2OI
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 \(\dfrac{BC}{2}=\dfrac{a}{2}\)
Lời giải:
a. Vì $BD\perp AC, CE\perp AB$ nên:
$\widehat{HDA}=\widehat{HEA}=90^0$
Tứ giác $AEHD$ có tổng 2 góc đối $\widehat{HDA}+\widehat{HEA}=90^0+90^0=180^0$ nên $AEHD$ là tứ giác nội tiếp
$\Rightarrow A,D,H,E$ cũng thuộc 1 đường tròn.
b.
$\widehat{CEB}=\widehat{BDC}=90^0$, mà 2 góc này cùng nhìn cạnh $BC$ nên $BEDC$ là tứ giác nội tiếp
$\Rightarrow B,D,E,C$ cùng thuộc 1 đường tròn (đpcm)
Hình vẽ:
![](data:image/png;base64,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)