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Giải bài 7 trang 89, 90 vở thực hành Toán 9 tập 2

Cho các điểm A, B, C, D trên đường tròn (O) như hình bên. Biết rằng CD là đường kính của (O) và (widehat {BOC} = {120^o}), hãy tính số đo các góc CAD và CDB.

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

Toán - Văn - Anh
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Đề bài

Cho các điểm A, B, C, D trên đường tròn (O) như hình bên. Biết rằng CD là đường kính của (O) và \(\widehat {BOC} = {120^o}\), hãy tính số đo các góc CAD và CDB.

Phương pháp giải - Xem chi tiết

Xét trong đường tròn (O), ta có: - Góc nội tiếp CDB và góc ở tâm BOC cùng chắn cung nhỏ BC nên \(\widehat {CDB} = \frac{1}{2}\widehat {BOC}\); - Vì CD là đường kính nên góc nội tiếp CAD chắn nửa đường tròn (O) nên tính được góc CAD.

Lời giải chi tiết

Xét trong đường tròn (O), ta có: - Góc nội tiếp CDB và góc ở tâm BOC cùng chắn cung nhỏ BC nên \(\widehat {CDB} = \frac{1}{2}\widehat {BOC} = {60^o}\); - Vì CD là đường kính nên góc nội tiếp CAD chắn nửa đường tròn (O) và do đó: \(\widehat {CAD} = {90^o}\).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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