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![](https://rs.olm.vn/images/avt/0.png?1311)
Xét ΔAHB vuông tại H có HM là đường cao ứng với cạnh huyền AB
nên \(AM\cdot AB=AH^2\left(1\right)\)
Xét ΔAHC vuông tại H có HN là đường cao ứng với cạnh huyền AC
nên \(AN\cdot AC=AH^2\left(2\right)\)
Từ (1) và (2) suy ra \(AM\cdot AB=AN\cdot AC\)
hay \(\dfrac{AM}{AC}=\dfrac{AN}{AB}\)
Xét ΔAMN và ΔACB có
\(\dfrac{AM}{AC}=\dfrac{AN}{AB}\)
\(\widehat{MAN}\) chung
Do đó: ΔAMN\(\sim\)ΔACB
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét ΔABH vuông tại H có HD là đường cao
nên \(BD\cdot BA=BH^2\)
=>\(BA\cdot3,6=6^2=36\)
=>BA=10(cm)
AD+DB=BA
=>AD+3,6=10
=>AD=6,4(cm)
ΔAHB vuông tại H
=>\(HA^2+HB^2=AB^2\)
=>\(HA=\sqrt{10^2-6^2}=8\left(cm\right)\)
Xét ΔAHB vuông tại H có HD là đường cao
nên \(HD\cdot AB=HA\cdot HB\)
=>\(HD\cdot10=6\cdot8=48\)
=>HD=4,8(cm)
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 \(AD\cdot AB=AE\cdot AC\)
=>\(\dfrac{AD}{AC}=\dfrac{AE}{AB}\)
Xét ΔADE và ΔACB có
AD/AC=AE/AB
\(\widehat{DAE}\) chung
Do đó: ΔADE đồng dạng với ΔACB
![](https://rs.olm.vn/images/avt/0.png?1311)
b: Xét ΔAHB vuông tại H có HM là đường cao ứng với cạnh huyền AB
nên \(AM\cdot AB=AH^2\left(1\right)\)
Xét ΔAHC vuông tại H có HN là đường cao ứng với cạnh huyền AC
nên \(AN\cdot AC=AH^2\left(2\right)\)
Từ (1) và (2) suy ra \(AM\cdot AB=AN\cdot AC\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có \(\widehat{AMH}=\widehat{ANH}\) nên tứ giác AMHN nội tiếp đường tròn đường kính AH.
b) Tứ giác AMHN nội tiếp nên \(\widehat{AMN}=\widehat{AHN}=\widehat{ACB}\Rightarrow\Delta AMN\sim\Delta ACB\left(g.g\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Trong tam giác AMN, ta có:
MN = AN.sin(∠MAN) (định lí sin)
Vì MN là hình chiếu vuông góc của D lên AB và AC, nên AN = AD.cos(∠BAC) và AM = AD.cos(∠CAB). Thay vào công thức trên, ta có:
MN = AD.cos(∠CAB).sin(∠BAC)
Do đó, để chứng minh MN = AD.sin(BAC), ta cần chứng minh rằng:
cos(∠CAB).sin(∠BAC) = sin(∠BAC)
Áp dụng định lí sin, ta có:
cos(∠CAB).sin(∠BAC) = sin(∠BAC).cos(∠CAB)
Vì cos(∠CAB) = cos(90° - ∠BAC) = sin(∠BAC), nên:
sin(∠BAC).cos(∠CAB) = sin(∠BAC).sin(∠BAC) = sin^2(∠BAC)
Vậy, MN = AD.sin(BAC).
Như vậy, đã chứng minh hai điều kiện trên.
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét ΔABC vuông tại A có sin C=AB/BC=3/5
=>cos C=căn 1-(3/5)^2=4/5
=>AC/BC=4/5
=>BC=20(cm)
\(AB=\sqrt{20^2-16^2}=12\left(cm\right)\)
ΔABC vuông tại A có AH là đường cao
nên CH*CB=CA^2
=>CH*20=16^2=256
=>CH=12,8(cm)
b: ΔHAB vuông tại H có HM là đường cao
nên AM*AB=AH^2
ΔHAC vuông tại H có HN là đường cao
nên AN*AC=AH^2
=>AM*AB=AN*AC
=>AM/AC=AN/AB
Xét ΔAMN vuông tại A và ΔACB vuông tại A có
AM/AC=AN/AB
Do đó: ΔAMN đồng dạng với ΔACB
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Vì HM là đường cao => \(HM\perp AB\)=> ^HMA = 900
Vì HN là đường cao => \(HN\perp AC\)=> ^HNA = 900
Xét tứ giác AMHN có :
^HMA + ^HNA = 900
mà ^HMA ; ^HNA đối nhau
Vậy tứ giác AMHN nội tiếp
b, Xét tam giác ABH vuông tại H, đường cao HM ta có :
\(AH^2=AM.AB\)(1)
Xét tam giác ACH vuông tại H, đường cao HN ta có :
\(AH^2=AN.AC\)(2)
từ (1) ; (2) suy ra : \(AM.AB=AN.AC\Rightarrow\frac{AM}{AC}=\frac{AN}{AB}\)
Xét tam giác AMN và tam giác ACB ta có :
^A chung
\(\frac{AM}{AC}=\frac{AN}{AB}\)( cmt )
Vậy tam giác AMN ~ tam giác ACB ( c.g.c )
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(BC=BH+HC=10\left(cm\right)\)
Áp dụng HTL: \(\left\{{}\begin{matrix}AH=\sqrt{BH\cdot HC}=4,8\left(cm\right)\\AB=\sqrt{BH\cdot BC}=6\left(cm\right)\end{matrix}\right.\)
\(\sin HCA=\dfrac{AB}{BC}=\dfrac{3}{5}\approx\sin37^0\\ \Rightarrow\widehat{HCA}\approx37^0\)
Lời giải:
a. Áp dụng hệ thức lượng trong tam giác vuông:
$AM.AB=AH^2$
$AN.AC=AH^2$
$\Rightarrow AM.AB=AN.AC$ (đpcm)
b.
Vì $AM.AB=AN.AC\Rightarrow \frac{AM}{AN}=\frac{AC}{AB}$
Xét tam giác $AMN$ và $ACB$ có:
$\widehat{A}$ chung
$\frac{AM}{AN}=\frac{AC}{AB}$ (cmt)
$\Rightarrow \triangle AMN\sim \triangle ACB$ (c.g.c)
Ta có đpcm.
Hình vẽ:
![](data:image/png;base64,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)