Cho tam giác nhọn ABC, 3 đường cao AA', BB', CC' cắt nhau tại H. C/m: H là tâm đường tròn nội tiếp ΔA'B'C'
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15 tháng 6 2022
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9 tháng 5 2022
a, Xét Δ ABD và Δ ABE, có :
\(\widehat{ADB}=\widehat{AEB}=90^o\)
\(\widehat{BAD}=\widehat{BAE}\) (góc chung)
=> Δ ABD ∾ Δ ABE (g.g)
b, Xét Δ EHB và Δ DHC, có :
\(\widehat{EHB}=\widehat{DHC}\) (đối đỉnh)
\(\widehat{HEB}=\widehat{HDC}=90^o\)
=> Δ EHB ∾ Δ DHC (g.g)
=> \(\dfrac{EH}{DH}=\dfrac{HB}{HC}\)
=> \(HB.HD=HC.HE\)
CM
31 tháng 12 2018
+ Các tam giác ABC và ABH có chung đáy AB nên tỉ số đường cao bằng tỉ số diện tích:
+ Tương tự:
Khi đó ta có