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

1. Hai đường tròn cắt 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 cắt nhau

Để có thể giải quyết dạng toán này, bạn cần thực hiện theo phương pháp sau:

  • Nối dây chung của hai đường tròn rồi dùng tính chất đường nối tâm của hai đường tròn
  • Hệ thức liên hệ: \(R - R' < OO' < R + R'\)

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