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Hai đường tròn tiếp xúc nhau là gì? Cách làm các bài toán có hai đường tròn tiếp xúc nhau - Toán 9

1. Hai đường tròn tiếp xúc nhau

Nếu hai đường tròn có đúng một điểm chung thì ta gọi đó là hai đường tròn cắt nhau.

Hai điểm chung đó là hai giao điểm của chúng.

Hai đường tròn (O;R) và (O;R’) cắt nhau khi \(R - R' < OO' < R + R'\) (với \(R > R'\))

Ví dụ: Cho OO’ = 5cm, khi đó hai đường tròn (O;4cm) và (O’;3cm) cắt nhau vì:

4cm – 3cm = 1cm < 5cm < 7cm = 4cm + 3cm.

2. Cách làm các bài toán có hai đường tròn tiếp xúc nhau

Để có thể giải quyết dạng toán này, chúng ta có thể sử dụng, áp dụng những định lý, tính chất sau:

  • Tiếp điểm nằm trên đường nối tâm
  • Hệ thức d = R + r
  • Khi làm ta có thể vẽ thêm tiếp tuyến chung của cả hai đường tròn (nếu cần).

3. Bài tập vận dụng

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