Cho tam giác ABC nhọn ; có 2 đường cao BD và CE cắt nhau tại H.
a. Chứng minh rằng 4 điểm A , D , H , E thuộc 1 đường tròn.
b. Chứng minh 4 điểm B , C , E , D thuộc 1 đường tròn.
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15 tháng 6 2022
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17 tháng 5 2021
a) Xét ΔAEB vuông tại E và ΔAFC vuông tại F có
\(\widehat{FAC}\) chung
Do đó: ΔAEB\(\sim\)ΔAFC(g-g)
Suy ra: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(Các cặp cạnh tương ứng tỉ lệ)
hay \(AE\cdot AC=AF\cdot AB\)(ĐPCM)
17 tháng 5 2021
b)
Ta có: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(cmt)
nên \(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)
Xét ΔAEF và ΔABC có
\(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)(cmt)
\(\widehat{FAE}\) chung
Do đó: ΔAEF\(\sim\)ΔABC(c-g-c)
CM
12 tháng 9 2017
Ta có: B O C ^ = 2 B A C ^ , C O A ^ = 2 C B A ^ , A O B ^ = 2 A C B ^
( góc ở tâm gấp 2 lần số đo góc nội tiếp cùng chắn 1 cung )
S = S O A B + S O B C + S O C A
= 1 2 O A . O B . sin A O B ^ + 1 2 O B . O C . sin B O C ^ + 1 2 O C . O A . sin C O A ^
S = 1 2 R 2 sin 2 A + sin 2 B + sin 2 C .
ĐÁP ÁN A
NY
0
PT
1
CM
10 tháng 3 2017
Vì M nằm trong tam giác ABC nên ta có:
Khi đó điểm M nhìn các cạnh AB,BC,CA của tam giác ABC dưới một góc bằng 120 °
Ta có thẻ dựng điểm M như sau:
Dựng cung chứa góc 120 ° vẽ trên đoạn BC
Dựng cung chứa góc 120 ° vẽ trên đoạn AC
Giao điểm thứ hai ngoài C của hai cung này là điểm M cần dựng
17 tháng 9 2023
a)
Nhận xét: H là một điểm nằm trong tam giác ABC.
b)
Nhận xét: H trùng với đỉnh A của tam giác ABC.
c)
Nhận xét: H nằm ngoài tam giác ABC.
a: Xét tứ giác AEHD có
\(\widehat{AEH}+\widehat{ADH}=180^0\)
nên AEHD là tứ giác nội tiếp
hay A,E,H,D cùng thuộc 1 đường tròn
b: Xét tứ giác BEDC có \(\widehat{BEC}=\widehat{BDC}\)
nên BEDC là tứ giác nội tiếp
hay B,E,D,C cùng thuộc 1 đường tròn