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Tiếp tuyến chung của hai đường tròn là gì? - Toán 9

1. Khái niệm Tiếp tuyến của đường tròn

Nếu đường thẳng và đường tròn tiếp xúc nhau thì đường thẳng được gọi là tiếp tuyến của đường tròn, điểm chung được gọi là tiếp điểm.

Điểm chung H của đường thẳng và đường tròn tiếp xúc với nhau goi là tiếp điểm.

Khi đó đường thẳng a còn gọi là tiếp tuyến của đường tròn (O) tại H.

Đường thẳng a tiếp xúc với đường tròn (O) tại H thì \(OH \bot a\).

2. Bảng tổng kết vị trí tương đối của hai đường tròn

Chú ý:
• Đường nối tâm (đường thẳng đi qua tâm 2 đường tròn) là trục đối xứng của hình tạo bởi hai đường tròn.
• Nếu hai đường tròn tiếp xúc nhau thì tiếp điểm nằm trên đường nối tâm.
• Nếu hai đường tròn cắt nhau thì đường nối tâm là đường trung trực của dây chung.

3. Tiếp tuyến chung của hai đường tròn

Tiếp tuyến chung của hai đường tròn là đường thẳng tiếp xúc với cả hai đường tròn đó. Ta có các trường hợp tiếp tuyến chung của hai đường tròn như sau:

1) Hai đường tròn cắt nhau có hai tiếp tuyến chung ngoài.

2) Hai đường tròn tiếp xúc ngoài có hai tiếp tuyến chung ngoài và một tiếp tuyến chung.

3) Hai đường tròn tiếp xúc trong chỉ có một tiếp tuyến chung.

4) Hai đường tròn ngoài nhau có hai tiếp tuyến chung ngoài và hai tiếp tuyến chung trong.

Chú ý:

• Hai đường tròn chứa nhau không có tiếp tuyến chung. • Hai đường tròn đồng tâm không có tiếp tuyến chung

4. Bài tập vận dụng

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