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![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1: Cho tam giác ABC vuông tại A, đường cao AH. a) Biết AH = 6cm, BH = 4,5cm.Tính AB, AC, BC,HC. b) Biết AB = 6cm, BH = 3cm.Tính AH và tính chu vi của các tam giác vuông trong hình.
Bài 1:
\(HC=\dfrac{AH^2}{HB}=\dfrac{36}{4.5}=8\left(cm\right)\)
BC=BH+CH=12,5cm
\(AB=\sqrt{4.5\cdot12.5}=7.5\left(cm\right)\)
\(AC=\sqrt{8\cdot12.5}=10\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1) Ta có △ABC có đường cao AH ⇒AH2=BH.HC⇒36=4,5.HC⇒HC=8(cm)
Ta có BC=HC+BH=4,5+8=12,5(cm)
Ta có AB2=BH.BC=4,5.12,5=56,25⇒AB=7,5(cm)
Ta có AC2=BC2-AB2=156,25-56,25=100⇒AC=10(cm)
Bài 2) Chắc bạn ghi sai đề rồi
![](https://rs.olm.vn/images/avt/0.png?1311)
a) xét tứ giác ABOC có
\(\widehat{ABO}+\widehat{ACO}=90^0\)(AB , AC tiếp tuyến)
=>\(\widehat{ABO}+\widehat{ACO}=180^0\)
=> tứ giác ABOC nội tiếp
=> \(\widehat{BOA}=\widehat{ACB}\)( chắn \(\widebat{BA}\))
b) ta có \(\hept{\begin{cases}AB=AC\left(cmt\right)\\OB=OC=R\end{cases}}\)
=> AO là đường trung trực của BC
=> \(AH\perp BC,HB=HC\)
=> \(\Delta IHB=\Delta IHC\left(c.g.c\right)\)
=>\(\widehat{HBI}=\widehat{ICH}=>\widebat{CI}=\widebat{BI}\)
\(=>\widehat{IBA}=\widehat{IBH}\)( chắn CI , BI )
=> IB là tia phân giác của góc ABC
c)xét tam giác OCA có \(CH\perp CA=>OC^2=OH.OA\)
mà \(OC=OD=>OC^2=OD^2\)
=>\(OD^2=OH.OA\)
mình làm lại nha
câu c, d nè :
c) áp dụng hệ thức lượng trong tam giác zuông ABO ta có
\(OH.OA=OB^2=OD^2=>OH.OA=OD^2\Leftrightarrow\)\(\frac{OH}{OD}=\frac{OD}{OA}=>\Delta OHD=\Delta ODA=>\widehat{OAD}=\widehat{ODH}\)
gọi J là là tâm đường tròn ngoại tiếp tam giác AHD
khi đó \(\widehat{OAD}=\frac{1}{2}\widehat{DJH}\)
zậy
\(\widehat{JDO}=\widehat{ODH}+\widehat{JDH}=\frac{1}{2}\widehat{DJH}+\widehat{JDH}=\frac{1}{2}\left(\widehat{DJH}+2\widehat{JDH}\right)=\frac{1}{2}.180^0=90^0\)
=> OD là ....
d) CHỉ ra M, N thuộc trung trực AH
theo cm ở cau C thì \(OD\perp JD\)nên J thuộc tiếp tuyến tại D của (O)
Mặt khác J là tâm đường tròn ngoại tiếp tam giác AHD nên J thuộc trung trực của AC
zậy J là giao điểm của tiếp tuyến tại D của (O) zà đường trung trực AD
=> J trùng E
zậy E là tâm đường tròn ngoại tiếp tam giác AHD nên E thuộc trung trực của AH
mặt khác M , N đều thuộc trung trực của AH nên M ,E ,N thẳng hàng
![](https://rs.olm.vn/images/avt/0.png?1311)
ý 1 câu a )
có ED vuông góc BC ; AH vuông góc BC => ED//AH => tam giác CDE đồng dạng vs tam giác CHA ( talet) (1)
xét tam giác CHA và tam giác CAB có CHA=CAB=90 độ ; C chung => tam giác CHA đồng dạng vs tam giác CAB ( gg) (2)
từ (1) và (2) =>tam giác CDE đồng dạng tam giác CAB ( cùng đồng dạng tam giác CHA )
có tam giác CDE đồng dạng tam giác CAB (cmt) => \(\frac{CE}{CB}=\frac{CD}{CA}\)
xét tam giác BAC và tam giác ADC có góc C chung và \(\frac{CE}{BC}=\frac{CD}{AC}\left(CMT\right)\) => tam giác BAC đồng dạng vs tam giác ADC ( trường hợp c-g-c) , mấy câu kia quên mịa nó r -.-
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(AH^2=HB.HC=50.8=400\)
\(\Rightarrow AH=20\left(cm\right)\)
\(S_{ABC}=\dfrac{1}{2}AH.BC=\dfrac{1}{2}.20\left(50+8\right)=\dfrac{1}{2}.20.58\left(cm^2\right)\)
mà \(S_{ABC}=\dfrac{1}{2}AB.AC\)
\(\Rightarrow AB.AC=20.58=1160\)
Theo Pitago cho tam giác vuông ABC :
\(AB^2+AC^2=BC^2\)
\(\Rightarrow\left(AB+AC\right)^2-2AB.AC=BC^2\)
\(\Rightarrow\left(AB+AC\right)^2=BC^2+2AB.AC\)
\(\Rightarrow\left(AB+AC\right)^2=58^2+2.1160=5684\)
\(\Rightarrow AB+AC=\sqrt[]{5684}=2\sqrt[]{1421}\left(cm\right)\)
Chu vi Δ ABC :
\(AB+AC+BC=2\sqrt[]{1421}+58=2\left(\sqrt[]{1421}+29\right)\left(cm\right)\)
Lời giải:
a.
Vì $\widehat{BAH}=\widehat{CAM}$ nên $\widehat{BAM]=\widehat{CAH}$
Ta có:
\(\frac{HB}{HC}=\frac{S_{BAH}}{S_{CAH}}=\frac{BA.AH.\sin \widehat{BAH}}{CA.AH.\sin \widehat{CAH}}=\frac{AB}{AC}.\frac{\sin \widehat{CAM}}{\sin \widehat{BAM}}(1)\)
\(1=\frac{BM}{CM}=\frac{S_{BAM}}{S_{CAM}}=\frac{AB.AM\sin \widehat{BAM}}{AC.AM.\sin \widehat{CAM}}=\frac{AB.\sin \widehat{BAM}}{AC\sin \widehat{CAM}}\)
\(\Rightarrow \frac{\sin \widehat{CAM}}{\sin \widehat{BAM}}=\frac{AB}{AC}(2)\)
Từ $(1);(2)\Rightarrow \frac{HB}{HC}=\frac{AB^2}{AC^2}$
b.
Đặt $AB=c; BC=a; CA=b$ thì theo phần a ta có:
$\frac{BH}{CH}=\frac{c^2}{b^2}\Rightarrow \frac{BH}{a}=\frac{c^2}{b^2+c^2}$
$\Rightarrow BH=\frac{ac^2}{b^2+c^2}$
$CH=\frac{ab^2}{b^2+c^2}$
Theo định lý Pitago:
$c^2-BH^2=b^2-CH^2$
$\Leftrightarrow c^2-\frac{a^2c^4}{(b^2+c^2)^2}=b^2-\frac{a^2b^4}{(b^2+c^2)^2}$
$\Leftrightarrow (b^2-c^2)=\frac{a^2(b^4-c^4)}{(b^2+c^2)^2}$
$\Leftrightarrow b^2-c^2=\frac{a^2(b^2-c^2)}{b^2+c^2}$
$\Leftrightarrow (b^2-c^2)(b^2+c^2)=a^2(b^2-c^2)$
$\Rightarrow b^2-c^2=0$ hoặc $b^2+c^2=a^2$
$\Leftrightarrow AB=AC$ hoặc tam giác $ABC$ vuông tại $A$.
Hình vẽ:
![](data:image/png;base64,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)