a. Em tự giải

b.

Ta có: \(\widehat{ABC}=\widehat{AQC}\) (cùng chắn AC) (1)

Do AQ là đường kính \(\Rightarrow\widehat{ACQ}\) là góc nt chắn nửa đường tròn

\(\Rightarrow\widehat{ACQ}=90^0\) \(\Rightarrow\widehat{ACQ}+\widehat{CAQ}=90^0\) (2)

Tam giác ABD vuông tại D \(\Rightarrow\widehat{BAD}+\widehat{ABC}=90^0\) (3)

(1);(2);(3) \(\Rightarrow\widehat{CAQ}=\widehat{BAD}\)

c.

\(\left\{{}\begin{matrix}\widehat{PAE}=\widehat{PAI}+\widehat{CAQ}\\\widehat{IAB}=\widehat{PAI}+\widehat{BAD}\\\widehat{CAQ}=\widehat{BAD}\left(cmt\right)\end{matrix}\right.\) \(\Rightarrow\widehat{PAE}=\widehat{IAB}\) (3)

Tứ giác BCEF nội tiếp (E và F cùng nhìn BC dưới 1 góc vuông)

\(\Rightarrow\widehat{ABI}+\widehat{CEF}=180^0\)

Mà \(\widehat{CEF}+\widehat{AEP}=180^0\)

\(\Rightarrow\widehat{AEP}=\widehat{ABI}\) (4)

(3);(4) \(\Rightarrow\Delta AEP\sim\Delta ABI\left(g.g\right)\)

\(\Rightarrow\dfrac{AP}{AI}=\dfrac{AE}{AB}\) (5)

AQ là đường kính \(\Rightarrow\widehat{ABQ}\) là góc nt chắn nửa đường tròn \(\Rightarrow\widehat{ABQ}=90^0\)

Xét 2 tam giác ABQ và AEH có: \(\left\{{}\begin{matrix}\widehat{ABQ}=\widehat{AEH}=90^0\\\widehat{BAQ}=\widehat{EAH}\left(\text{theo (3)}\right)\end{matrix}\right.\)  \(\Rightarrow\Delta ABQ\sim\Delta AEH\left(g.g\right)\)

\(\Rightarrow\dfrac{AE}{AB}=\dfrac{AH}{AQ}\) (6)

(5);(6) \(\Rightarrow\dfrac{AH}{AQ}=\dfrac{AP}{AI}\) \(\Rightarrow\dfrac{AP}{AH}=\dfrac{AI}{AQ}\)

\(\Rightarrow PI||HQ\) (định lý Talet đảo)

0 sights

1 awesome

2 enthusiastic

3 achievement

4 competitor

5 unstable

6 steadily

7 boring

8 strengthen

9 additional

10 likelihood

Bạn tham khảo lời giải tại đây:

https://hoc24.vn/cau-hoi/giai-pt-sqrtx-2sqrt4-x2x2-5x-1.219493072549

a) 9/5 + 2/5 x 4/6 = 9/5 + 4/15 = 27/15 + 4/15 = 31/15
b) 3/8 x 2 - 6/7 x 1/3 = 3/4 - 2/7 = 21/28 - 8/28 = 13/28

a) 9/5 + 2/5 x 4/6 = 9/5 + 4/15 = 27/15 + 4/15 = 31/15
b) 3/8 x 2 - 6/7 x 1/3 = 3/4 - 2/7 = 21/28 - 8/28 = 13/28

1. They celebrate it in the first month of spring. 

2. People often clean their house. 

3. It means fire.

4. Yes, it is. 

1. They celebrate it in the first month of spring. 

2. People often clean their house. 

3. It means fire.

4. Yes, it is. 

1. It is easy for everyone to get access to the Internet

2.Solar

1 not

2 It is easy for everyone to get access to the internet

3 C

Mk quay dọc ra cho dễ nhìn nhé

I, 

1. best

2. happiest

3. faster

4. more colourful

5. better

6. good

7. least

8. prettiest

9. the best

10. the sicker

I/

1. best

2. happiest

3. faster

4. more colourful

5. better

6. good

7. least

8. prettier

9. the better

10. the sticker

II/

3. more slowly

III/

1. Sarah is younger than Tim

2. Your house is smaller than ours

3. Bill is shorter than David

4. My marks are better than Jack's

5. That book is as expensive as this one

6. My bike is faster than yours