a: Xét tứ giác BHCK có

M là trung điểm chung của BC và HK

=>BHCK là hình bình hành

=>BH//CK

mà BH\(\perp\)AC

nên CK\(\perp\)CA

b: ΔAFH vuông tại F

mà FI là đường trung tuyến

nên \(FI=\dfrac{AH}{2}\left(1\right)\)

ΔAEH vuông tại E

mà EI là đường trung tuyến

nên \(EI=\dfrac{AH}{2}\left(2\right)\)

Từ (1),(2) suy ra FI=EI

=>I nằm trên đường trung trực của EF(3)

Ta có: ΔBFC vuông tại F

mà FM là đường trung tuyến

nên FM=MB=MC=BC/2(4)

Ta có: ΔBEC vuông tại E

mà EM là đường trung tuyến

nên EM=MB=MC=BC/2(5)

Từ (4),(5) suy ra ME=MF

=>M nằm trên đường trung trực của EF(6)

Từ (3),(6) suy ra IM là đường trung trực của EF

BHCK là hình bình hành

=>BK//CH

mà CH\(\perp\)AB

nên BK\(\perp\)BA

=>B nằm trên đường tròn đường kính AK(7)

Ta có: CK\(\perp\)CA

=>C nằm trên đường tròn đường kính AK(8)

Từ (7),(8) suy ra A,B,K,C cùng thuộc (O)

Xét (O) có

\(\widehat{ABC}\) là góc nội tiếp chắn cung AC

\(\widehat{AKC}\) là góc nội tiếp chắn cung AC

Do đó: \(\widehat{ABC}=\widehat{AKC}\)

MB=MC=ME=MF

=>BFEC nội tiếp (M)

=>\(\widehat{AEF}=\widehat{ABC}\left(=180^0-\widehat{BFE}\right)\)

\(\widehat{AEF}+\widehat{KAC}=90^0-\widehat{AKC}+\widehat{ABC}=90^0-\widehat{ABC}+\widehat{ABC}=90^0\)

=>AK\(\perp\)EF

Yêu cầu của bài toán là gì vậy em?

\(\left(x^2+3x\right)^2-2\left(x^2+3x\right)-8\)

\(=\left(x^2+3x\right)^2-4\left(x^2+3x\right)+2\left(x^2+3x\right)-8\)

\(=\left(x^2+3x-4\right)\left(x^2+3x+2\right)\)

\(=\left(x+4\right)\left(x-1\right)\cdot\left(x+2\right)\left(x+1\right)\)

1. Your kitchen is bigger than mine.
2. Dave is the tallest in the class.
3. Dad speaks English better than Mum.
4. Hoa can’t cook as well as Lan.
5. That restaurant is the best in the city.
6. That watch is better than this one.
7. My sister writes less carefully than she did.
8. This is the most interesting story I have ever read.
9. I’ve never known a girl more beautiful than her.
10. Tom drives more carefully than Peter.

1. My kitchen is smaller than yours.
 Your kitchen …is bigger than mine……………………………………………………………………………
2. No one in the class is taller than Dave.
 Dave is …………the tallest student in the class…………………………………………………………… 
3. Mum doesn’t speak English as well as Dad.
 Dad ……speaks English better than Mum………………………………………………………………………….………
4. Lan is better cook than Hoa.
 Hoa can’t  ……cook as well as Lan……………………………………………………………………...……
5. No restaurant in the city is better than that one.
 That restaurant is ……………the best in the city……………………………………………………………

giúp mình gấp vs ạ . mình đang cần ạ

81. It’s not possible to play tennis because of the rain. (makes)

-> The rain ……makes it impossible…………………………………… to play tennis.

82. To Alan’s amazement, the passport office was closed when he arrived. (find)

-> Alan was ……amazed to find that……………………..………. the passport of office was closed when he arrived.

83. They think the chair was made in the 17^th century. (thought)

-> The chair is ………thought to be made……………………………… in the 17^th century.

1. It is quiet simple to cook Thang Co.

2. Do you like to live in the big city or in the countryside?

3. Traffic is becoming better.

4. Life in the country is changing better.

5. Mr. Hung is arriving in Ho Chi Minh city tonight.

1 It is quite simple to cook Thang Co

2 Do you live living in the big city or the coutryside?

3 The traffic is becomig better

4 Life in the country is changing better

5 Mr Hugiss arriving in HCM city tonight

1 I never play extreme sports without wearing a helmet

2 We had a little food left in the market, so we made a nice dinner last night

1. He loves taking photos of beautiful views while climbing. (keen)

➙____He is keen on taking photos of beautiful views while climbing_________________________________________

2. We usually collect eggs from the chicken coop every day. (habit)

➙_____We are in the habit of collecting eggs from the chicken coop everyday________________________________________

3. The festival is too far to walk there in just a few minutes. (enough)

➙____The festival is not near enough for us to walk there in just a few minutes_________________________________________