Tam giác \(A B C\) cân tại \(A\) nên \(A B = A C = 12\) cm.

Xét tam giác \(A B C\), áp dụng tính chất tia phân giác ta có:

\(\frac{A D}{D B} = \frac{A C}{C B} = \frac{12}{6} = 2\)

Suy ra \(\frac{A D}{A B} = \frac{2}{3}\) suy ra \(A D = \frac{2}{3} . 12 = 8\) (cm)

Do đó, \(D B = 12 - 8 = 4\) (cm).

Xét tam giác \(A B C\), áo dụng tính chất tia phân giác trong tam giác, ta có: 

\(\frac{A M}{M B} = \frac{A C}{C B} = \frac{A B}{C B} = \frac{A N}{N C} \left(\right. = \frac{b}{a} \left.\right)\)

Vậy \(M N\) // \(B C\) (Định lí đảo của định lí Thalès)

Suy ra \(\frac{M N}{B C} = \frac{A M}{A B} = \frac{b}{b + a}\) (Định lí Thalès)

Vậy nên \(M N = \frac{a b}{a + b} .\)

1. The Muong earn their living by farming and raising animals.

2. They are in the habit of exercising after work

Topic 1 :

Living a healthy lifestyle brings many benefits to our lives. First, it helps prevent serious illnesses like heart disease and diabetes. When we eat a balanced diet and exercise regularly, our immune system becomes stronger. Second, a healthy lifestyle improves mental health. We feel more energetic, positive, and less stressed after doing sports. Finally, it helps us maintain a fit body weight. In short, staying healthy allows us to enjoy life more and live longer.

Topic 2 :

The Lunar New Year is a big festival in Viet Nam .In my family, people clean and decorate my house. People buys flowers , hang red decorations and prepare traditional food. Families cook tradional food like Banh Chung .In the last day of year , family gather to cook Banh Chung and spend time together . In the first day of new year , children recives lucky money and visit ralatives to give New Year wishes .The Lunar New Year is also very special occasion for all of us

Topic 3 :

I help my family in various ways to contribute to their well-being. Firstly, I assist with household chores such as cleaning, cooking, and doing laundry. This helps to lighten the workload for everyone and ensures a clean and comfortable living environment. Additionally, I offer my support and lend a listening ear whenever someone in my family needs to talk or share their problems. I also help with grocery shopping and running errands, making sure that everyone's needs are met. Lastly, I try to be responsible and respectful towards my family members, showing them love and appreciation. These small acts of kindness and assistance go a long way in creating a harmonious and supportive family dynamic.

1. If you don't drink more water , you will get more acne .

2. My sister wants to see the terracced fields in Sa Pa .

3. Unless he spends time on his phone , he will complete his work .

Stress is a common problem for many students , and it can be caused by various factions. One of the main causes is peer pressure as students often feel the need in or meet the expectations of their friends. Anorther significant cause is having too much schoolwork , which can lead to feelings of being overwhelmed. Additionally spendding too much time on social media and being a victim of bullying can also contribute to stress . To cope with these issues , there are several possible solutions . Studentcan try to stay calm and relaxed by practicing mindfulness or deep breathing . Talking to teachers or school counselors can also be helpful , as they can provide support and guidance.Limiting the use of smartphones and social media can reduce feelings of inadequacy and avoiding bullies whenever possible is crucial for your well - being