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Lý thuyết Vị trí tương đối của hai đường tròn Toán 9 Kết nối tri thức

1. Hai đường tròn cắt nhau

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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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. Hai đường tròn tiếp xúc với nhau

Nếu hai đường tròn có duy nhất một điểm chung thì ta nói đó là hai đường tròn tiếp xúc với nhau.

Điểm chung đó gọi là tiếp điểm của chúng.

+ Hai đường tròn (O;R) và (O’;R’) tiếp xúc ngoài khi \(OO' = R + R'\).+ Hai đường tròn (O;R) và (O’;R’) tiếp xúc trong khi \(OO' = R - R'\left( {R > R'} \right)\).Nếu hai đường tròn tiếp xúc với nhau thì tiếp điểm thẳng hàng với hai tâm.

Ví dụ:

Cho OO’ = 5cm, khi đó hai đường tròn (O;3cm) và (O’;2cm) tiếp xúc ngoài với nhau vì 5cm = 3cm + 2cm.Cho OO’ = 3cm, khi đó hai đường tròn (O;8cm) và (O’;5cm) tiếp xúc trong với nhau vì 3cm = 8cm - 5cm.

3. Hai đường tròn không giao nhau

Nếu hai đường tròn không có điểm chung nào thi ta nói đó là hai đường tròn không giao nhau.

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

- Đường tròn (O;R) đựng 🔯đường tròn (O’;R’) khi \(R > R'\) và \(OO' < R - R'\).

Khi O trùng với O’ và \(R \ne R'\) thì ta có hai đường tròn đồng tâm.

Ví dụ: Cho đường tròn (O;3cm) và (O’;4cm) có \(OO' > 8cm\) thì \(OO' = 8cm > 3cm + 4cm = R + R'\) nên (O;3cm) và (O’;4cm) là hai đường tròn ngoài nhau.

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