Cho tam giác cân ABC có đáy = a, cạnh bên AB = AC. Đường phân giác góc B cắt AC tại N, đường phân giác góc C cắt AB tại M.

Theo tính chất đường phân giác trong tam giác: Trong tam giác ABC, phân giác góc C:

AM/MB = AB/BC = b/a

Suy ra:

AM/AB = AN/AC = b/a+b

Do đó M và N chia hai cạnh bên theo cùng tỉ lệ nên MN // BC. Hai tam giác AMN và ABC đồng dạng, nên:

MN/BC = AM/AB = b/a+b

Vì BC = a, suy ra:

MN = b/a+b × a = ab/a+b

Kết luận: MN = ab/ a+b

Xét tam giác ABC cân tại A nên AB = AC = 12 cm. Phân giác góc C cắt AB tại D. Theo tính chất đường phân giác trong tam giác, ta có tỉ số giữa hai đoạn thẳng trên cạnh bị chia bằng tỉ số hai cạnh kề góc phân giác:

AD/DB = AC/BC = 12/6 = 2

Đặt AD = 2x, DB = x. Khi đó:

AD + DB = AB. Suy ra:

2x + x = 12

3x = 12

x = 4

Vậy: AD = 8 cm, DB = 4 cm

A healthy lifestyle brings many benefits to our life. It helps us stay strong and avoid many diseases. Eating healthy food, exercising regularly and sleeping enough make our body and mind better. When we live healthily, we feel happier and more active. Moreover, a healthy lifestyle helps us study and work more effectively every day.

1, Muong earns a living by farming and raising animals.

2, They are in the habit of exercising after work.

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

2, My sister wants to see the terraced fields, so she is going to Sa Pa.

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

A healthy lifestyle brings many benefits to our life. It helps us stay strong and avoid many diseases. Eating healthy food, exercising regularly and sleeping enough make our body and mind better. When we live healthily, we feel happier and more active. Moreover, a healthy lifestyle helps us study and work more effectively every day.

Bài 2:

1, Muong earn a living by farming and raising animals.

2, They are in the habit of exercising after work.

Bài 2:

1, Muong earn a living by farming and raising animals.

2, They are in the habit of exercising after work.