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1.

\(cosA=\dfrac{b^2+c^2-a^2}{2bc}=\dfrac{1}{2}\Rightarrow\widehat{A}=60^o\)

\(S=\dfrac{1}{2}bc.sinA=\dfrac{1}{2}.8.5.sin60^o=10\sqrt{3}\)

\(S=\dfrac{1}{2}a.h_a=\dfrac{1}{2}.7.h_a=10\sqrt{3}\Rightarrow h_a=\dfrac{20\sqrt{3}}{7}\)

\(2R=\dfrac{a}{sinA}=\dfrac{7}{\dfrac{\sqrt{3}}{2}}=\dfrac{14\sqrt{3}}{3}\Rightarrow R=\dfrac{7\sqrt{3}}{3}\)

\(S=pr=\dfrac{a+b+c}{2}.r=10r=10\sqrt{3}\Rightarrow r=\sqrt{3}\)

\(m_a^2=\dfrac{b^2+c^2}{2}-\dfrac{a^2}{4}=\dfrac{129}{4}\Rightarrow m_a=\dfrac{\sqrt{129}}{2}\)

6.

a, Công thức trung tuyến:

\(AM^2=c^2=\dfrac{b^2+c^2}{2}-\dfrac{a^2}{4}=\dfrac{2b^2+2c^2-a^2}{4}\Rightarrow a^2=2\left(b^2-c^2\right)\)

b, \(a^2=2\left(b^2-c^2\right)\Rightarrow\dfrac{2\left(b^2-c^2\right)}{a^2}=1\)

\(\Leftrightarrow2\left(\dfrac{b^2}{a^2}-\dfrac{c^2}{a^2}\right)=1\)

\(\Leftrightarrow2\left(\dfrac{b^2}{a^2}.sin^2A-\dfrac{c^2}{a^2}.sin^2A\right)=sin^2A\)

\(\Leftrightarrow2\left(sin^2B-sin^2C\right)=sin^2A\)

Hay \(sin^2A=2\left(sin^2B-sin^2C\right)\)

Câu 7: Hình bạn tự vẽ

Giả sử hai trung tuyến \(AA_1;BB_1\) vuông góc với nhau. Gọi I là giao điểm của hai trung tuyến

Ta có: \(IA^2+IB^2=AB^2\)\(\Leftrightarrow\left(\dfrac{2}{3}m_a\right)^2+\left(\dfrac{2}{3}m_b\right)^2=c^2\)\(\Leftrightarrow4m_a^2+4m_b^2=9c^2\Leftrightarrow2\left(b^2+c^2\right)-a^2+2\left(a^2+c^2\right)-b^2=9c^2\Leftrightarrow a^2+b^2=5c^2\)(đúng với giả thiết)

suy ra giả sử là đúng . Vậy hai trung tuyến \(AA_1;BB_1\) vuông góc với nhau

...eating lots of food, she is still very slim

...is it from Hanoi to HCM city?

...interested in English

...dance very well 

...the weather was bad, we went to school

...eating lots of food, she is still very slim

did - go

went - didn't enjoy 

take

takes

goes

playing

am wanting

used to play - was

did - ever heard

will - travel

will be taking

will spend

haven't seen

she is interested in reading comic

Tomorrow in this time I wil be lieing on the beach

My car isn't as expensive as his

She has started live in Paris since 2005

A new dam will build near the rive next year

She is interested in reading comic.

Tomorrow in this time I wil be lying on the beach.

My car isn't as expensive as his.

She has started living in Paris since 2005.

A new dam will be built near the rive next year.

1. used to

2. will be taking

3. am watching

4. will go

5. will be washing

6. will be replaced

7. do

8. has visited

9. haven't bought

10. swim

1. had used

2. will be taking

3. will be watching

4. will go

5. will be washing

6. will be replaced

7. do

8. has visited

9. have not bought

10. swim

1. used to

2. will be taking

3. am watching

4. will go

5. will be washing

6. will be replaced

7. do

8. has visited

9. haven't bought

10. swim

1. used to

2. will be taking

3. am watching

4. will go

5. will be washing

6. will be replaced

7. do

8. has visited

9. haven't bought

10. swim

Why did you stay at home?

Who are they waiting for?

What is she doing at the moment?

How did she go to Ha Noi? 

When does your father often watch TV?