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![](https://rs.olm.vn/images/avt/0.png?1311)
a) Vì AI^2=AD.AE nên để chứng minh AI^2=DE.AK ta chứng minh AD.AE=DE.AK bằng cách chứng minh hai tam giác ADE và KAE đồng dạng.
b) Trong tam giác vuông AIK có sinAIK = AK/AI = AI/DE ( theo đẳng thức ở câu a)
Mà AI là đường trung tuyến ứng với cạnh huyền nên AI = DE/2
Do đó sinAIK = 1/2 suy ra góc AIK bằng 30 độ.
![](https://rs.olm.vn/images/avt/0.png?1311)
a: BC=BH+CH
=2+8
=10(cm)
Xét ΔABC vuông tại A có AH là đường cao
nên \(AH^2=HB\cdot HC\)
=>\(AH=\sqrt{2\cdot8}=4\left(cm\right)\)
Xét ΔABC vuông tại A có AH là đường cao
nên \(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot CB\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}AB=\sqrt{2\cdot10}=2\sqrt{5}\left(cm\right)\\AC=\sqrt{8\cdot10}=4\sqrt{5}\left(cm\right)\end{matrix}\right.\)
b: Xét tứ giác ADHE có
\(\widehat{ADH}=\widehat{AEH}=\widehat{DAE}=90^0\)
=>ADHE là hình chữ nhật
=>DE=AH
c: ΔHDB vuông tại D
mà DM là đường trung tuyến
nên DM=HM=MB
\(\widehat{EDM}=\widehat{EDH}+\widehat{MDH}\)
\(=\widehat{EAH}+\widehat{MHD}\)
\(=90^0-\widehat{C}+\widehat{C}=90^0\)
=>DE vuông góc DM
![](https://rs.olm.vn/images/avt/0.png?1311)
a: ΔABC vuông tại A
=>\(BC^2=AB^2+AC^2\)
=>\(BC=\sqrt{9^2+12^2}=15\left(cm\right)\)
Xét ΔABC vuông tại A có AH là đường cao
nên \(\left\{{}\begin{matrix}AH\cdot BC=AB\cdot AC\\BH\cdot BC=AB^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AH=\dfrac{9\cdot12}{15}=7.2\left(cm\right)\\BH=\dfrac{9^2}{15}=5.4\left(cm\right)\end{matrix}\right.\)
b:
ΔAHB vuông tại H có HD là đường cao
nên \(HD\cdot AB=HA\cdot HB\)
ΔAHC vuông tại H có HE là đường cao
nên \(HE\cdot AC=HA\cdot HC\)
\(HD\cdot AB+HE\cdot AC\)
\(=HA\cdot HB+HA\cdot HC=HA\cdot\left(HB+HC\right)\)
\(=HA\cdot BC=AB\cdot AC\)
c: Xét tứ giác ADHE có \(\widehat{ADH}=\widehat{AEH}=\widehat{DAE}=90^0\)
=>ADHE là hình chữ nhật
ΔABC vuông tại A có AM là trung tuyến
nên AM=MB=MC
\(\widehat{IEA}+\widehat{IAE}=\widehat{DEA}+\widehat{IAC}\)
\(=\widehat{DHA}+\widehat{MCA}\)
\(=\widehat{ABC}+\widehat{ACB}=90^0\)
=>AM vuông góc DE tại I
ΔADE vuông tại A có AI là đường cao
nên \(\dfrac{1}{AI^2}=\dfrac{1}{AE^2}+\dfrac{1}{AD^2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét tứ giác ADHE có:
\(\widehat{BAC}=\widehat{ADH}=\widehat{AEH}=90^0\)
=> Tư giác ADHE là hình chữ nhật
\(\Rightarrow DE=AH\left(1\right)\)
Áp dụng HTL trong tam giác ABC vuông tại A có đường cao AH
\(AH^2=HB.HC\left(2\right)\)
\(\left(1\right),\left(2\right)\Rightarrow DE^2=HB.HC\)
Xét ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC
nên \(AH^2=HB\cdot HC\left(1\right)\)
Xét tứ giác ADHE có
\(\widehat{ADH}=\widehat{AEH}=\widehat{DAE}=90^0\)
Do đó: ADHE là hình chữ nhật
Suy ra: AH=DE(2)
Từ (1) và (2) suy ra \(DE^2=HB\cdot HC\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b: Xét ΔAHB vuông tại H có HD là đường cao
nên \(AD\cdot AB=AH^2\left(1\right)\)
Xét ΔAHC vuông tại H có HE là đường cao
nên \(AE\cdot AC=AH^2\left(2\right)\)
Từ (1) và (2) suy ra \(AD\cdot AB=AE\cdot AC\)
Theo đkđb thì $AI^2=AD.AE$. Vì vậy, nếu muốn $AI^2=DE.AE$ thì $AD=DE$ (điều này vô lý vì $AD<DE$ theo tính chất cạnh huyền trong tam giác vuông.
Hình vẽ:
![](data:image/png;base64,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)