Cho tam giác ABC vuông tại A có BC=10cm, AH =4cm ( AH là đường cao ). Gọi I,K là chân đường vuông góc kẻ từ H xuống các cạnh AB,AC. Tính chu vi và diện tích tứ giác AIHK
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Tứ giác AIHK có góc H=K=I=A=90độ
=> AIHK LÀ HÌNH CHỮ NHẬT ( tỨ GIÁC CÓ 3 GÓC VUÔNG)
![](https://rs.olm.vn/images/avt/0.png?1311)
b: Xét tứ giác AEHF có
\(\widehat{AEH}=\widehat{AFH}=\widehat{EAF}=90^0\)
Do đó: AEHF là hình chữ nhật
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Xét ΔABC vuông tại A có AH là đường cao
nên \(AH^2=HB\cdot HC\)
=>\(AH=\sqrt{4\cdot9}=6\left(cm\right)\)
Xét tứ giác ADHE có \(\widehat{ADH}=\widehat{AEH}=\widehat{DAE}=90^0\)
=>ADHE là hình chữ nhật
=>DE=AH=6(cm)
b: Xét tứ giác ADHE có
\(\widehat{ADH}+\widehat{AEH}=180^0\)
=>ADHE là tứ giác nội tiếp
=>A,D,H,E cùng nằm trên 1 đường tròn
c: \(\widehat{CAK}+\widehat{BAK}=90^0\)
\(\widehat{CKA}+\widehat{HAK}=90^0\)
mà \(\widehat{BAK}=\widehat{HAK}\)
nên \(\widehat{CAK}=\widehat{CKA}\)
=>ΔCAK cân tại C
ΔCAK cân tại C
mà CI là đường trung tuyến
nên CI là đường cao
=>CI vuông góc AK
Lời giải:
Ta có:
$AB.AC=AH.BC=40$
$AB^2+AC^2=BC^2=100$
$\Rightarrow (AB+AC)^2=AB^2+AC^2+2AB.AC=180$
$\Rightarrow AB+AC=6\sqrt{5}$
Theo định lý Viet đảo, $AB,AC$ là nghiệm của pt $X^2-6\sqrt{5}X+40=0$
$\Rightarrow AB=4\sqrt{5}; AC=2\sqrt{5}$ (giả sử $AB>AC$)
Dễ thấy $AIHK$ là hình chữ nhật do có 3 góc vuông $\widehat{A}=\widehat{I}=\widehat{K}=90^0$
$\Rightarrow IK=AH=4$
Theo định lý Pitago: $AI^2+AK^2=IK^2=16(1)$
Mặt khác, theo hệ thức lượng trong tam giác vuông:
$AI.AB=AH^2$
$AK.AC=AH^2$
$\Rightarrow AI.AB=AK.AC\Rightarrow \frac{AI}{AK}=\frac{AC}{AB}=\frac{2\sqrt{5}}{4\sqrt{5}}=\frac{1}{2}(2)$
Từ $(1);(2)\Rightarrow AI=\frac{4\sqrt{5}}{5}; AK=\frac{8\sqrt{5}}{5}$ (cm)
Chu vi AIHK:
$P=2(AI+AK)=2(\frac{4\sqrt{5}}{5}+\frac{8\sqrt{5}}{5})=\frac{24\sqrt{5}}{5}$ (cm)
Diện tích AIHK:
$S=AI.AK=\frac{4\sqrt{5}}{5}.\frac{8\sqrt{5}}{5}=6,4$ (cm vuông)
Hình vẽ:
![](data:image/png;base64,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)