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Lý thuyết Góc nội tiếp Toán 9 Kết nối tri thức

Định nghĩa góc nội tiếp Góc nội tiếp là góc có đỉnh nằm trên đường tròn và hai cạnh chứa hai dây cung của đường tròn đó. Cung nằm bên trong góc được gọi là cung bị chắn.

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

Toán - Văn - Anh
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Định nghĩa góc nội tiếp

Góc nội tiếp 𓂃là góc có đỉnh nằm trên đường tròn và hai cạnh chứa hai dây cung của đường tròn đó.

Cung nằm bên trong góc được gọi là cung bị chắn.

Ví dụ:

- Góc BAC là góc nội tiếp của đường tròn (O);- Góc nội tiếp BAC chắn cung $\overset\frown{BmC}$.

Định lí mối liên hệ giữa góc nội tiếp với cung bị chắn

Trong một đường tròn, số đo của góc nội tiếp bằng nửa số đo của cung bị chắn.

Ví dụ:

\(\widehat {BAC} = \frac{1}{2}\)sđ$\overset\frown{BmC}=\frac{1}{2}\widehat{BOC}$.

Nhận xét: ๊Đối với góc nội tiếp của cùng một đường tròn hoặc của hai đường tròn bằng nhau, ta có các khẳng định sau:

+ Các góc nội tiếp bằng nhau chắn các cung bằng nhau.+ Các góc nội tiếp cùng chắn một cung hoặc chắn các cung bằng nhau thì bằng nhau.+ Các góc nội tiếp chắn cung nhỏ thì có số đo bằng nửa số đo của góc ở tâm chắn cùng một cung.+ Góc nội tiếp chắn nửa đường tròn là góc vuông.

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