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Giải bài 1 trang 88 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho ba điểm A, B, C cùng nằm trên đường tròn (O) sao cho AC đi qua O. Vẽ đoạn thẳng DE tiếp xúc với (O) tại A. Cho biết (widehat {BAD} = {78^o}). Tính số đo (widehat {BCA}).

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

Toán - Văn - Anh
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Đề bài

Cho ba điểm A, B, C cùng nằm trên đường tròn (O) sao cho AC đi qua O. Vẽ đoạn thẳng DE tiếp xúc với (O) tại A. Cho biết \(\widehat {BAD} = {78^o}\). Tính số đo \(\widehat {BCA}\).

 

Phương pháp giải - Xem chi tiết

Dựa vào: DE tiếp xúc với (O) tại A 🥃nên DE là tiếp tuyến và vuông góc với bán kính đi qua điểm A.

Lời giải chi tiết

DE tiếp xúc với (O) tại A, suy ra \(OA \bot DE\). Ta có:

🎀\(\widehat {BAO} = {90^o} - \widehat {BAD} = {90^o} - {78^o} = {12^o}\)

hay \(\widehat {BAC} = {12^o}\).

𝓀Ta có OB = OA = OC = R, suy ra tam giác ABC vuông tại B, suy ra

🧸\(\widehat {BCA} = {90^o} - \widehat {BAC} = {90^o} - {12^o} = {78^o}\).

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

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