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Giải bài 14 trang 106 sách bài tập toán 9 - Cánh diều tập 1

Cho đường tròn (O;R) và điểm A sao cho OA = 2R. Kẻ tiếp tuyến AB của đường tròn (O; R) với B là tiếp điểm (hình 14). Tính độ dài đoạn thẳng AB theo R.

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

Toán - Văn - Anh
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Đề bài

Cho đường tròn (O;R) và điểm A sao cho OA = 2R. Kẻ tiếp tuyến AB của đường tròn (O; R) với B là tiếp điểm (hình 14). Tính độ dài đoạn thẳng AB theo R.

Phương pháp giải - Xem chi tiết

Áp dụng định lý Pythagore trong tam giác vuông OBA.

Lời giải chi tiết

Do tiếp tuyến AB của đường tròn (O; R) nên OB vuông góc với AB. Áp dụng định lý Pythagore trong tam giác vuông OBA ta có \(AB = \sqrt {O{A^2} - O{B^2}}  = \sqrt {{{\left( {2R} \right)}^2} - {R^2}}  = R\sqrt 3 \). Vậy \(AB = R\sqrt 3 \).

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

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