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Số đo của cung với số đo góc ở tâm có mối liên hệ gì? Cách tính số đo góc ở tâm và số đo cung bị chắn - Toán 9

1. Khái niệm góc ở tâm

Góc ở tâm là góc có đỉnh trùng với tâm của đường tròn.

- Nếu \(0^\circ  < \alpha  < 180^\circ \) thì cung nằm bên trong góc được gọi là cung nhỏ, cung nằm bên ngoài góc được gọi là cung lớn. - Nếu \(\alpha  = 180^\circ \) thì mỗi cung là một nửa đường tròn.

2. Mối liên hệ giữa số đo của cung và số đo góc ở tâm

- Số đo của cung nhỏ bằng số đo của góc ở tâm chắn cung đó. - Số đo cung lớn bằng hiệu giữa \(360^\circ \) và số đo của cung nhỏ có chung hai mút.

3. Cách tính số đo góc ở tâm và số đo cung bị chắn

Số đo của một cung được xác định như sau:

- Số đo của nửa đường tròn bằng \(180^\circ \). - Số đo của cung nhỏ bằng số đo của góc ở tâm chắn cung đó. - Số đo cung lớn bằng hiệu giữa \(360^\circ \) và số đo của cung nhỏ có chung hai mút.

Ví dụ: Số đo của cung AB được kí hiệu là sđ$\overset\frown{AB}$.

sđ$\overset\frown{AmB}=\widehat{AOB}=\alpha $; sđ$\overset\frown{AnB}=360{}^\circ -\alpha $.

Chú ý:

- Cung có số đo \(n^\circ \) còn được gọi là cung \(n^\circ \). Cả đường tròn được coi là cung \(360^\circ \). Đôi khi ta cũng coi một điểm là cung \(0^\circ \). - Hai cung trên một đường tròn gọi là bằng nhau nếu chúng có cùng số đo.

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