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Giải bài tập 3 trang 89 SGK Toán 9 tập 1 - Chân trời sáng tạo

Trong Hình 16, AB = 9; BC = 12; AC = 15 và BC là đường kính của đường tròn (O). Chứng minh AB là tiếp tuyến của đường tròn (O).

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

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Đề bài

ꦚTrong Hình 16, AB = 9; BC = 12; AC = 15 và BC là đường kính của đường tròn (O). Chứng minh AB là tiếp tuyến của đường tròn (O).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh \(\widehat {CBA} = {90^o}\) hay \(AB \bot BO\) suy ra AB là tiếp tuyến.

Lời giải chi tiết

Theo hình ta có: AB = 9; BC = 12; AC = 15

Suy ra AC2 = AB2 + BC2 nên tam giác ABC vuông tại B

Hay \(\widehat {CBA} = {90^o}\) suy ra \(AB \bot BC\) Mà \(O \in BC\) nên \(AB \bot BO\) Vậy AB đi qua B (B \( \in (O)\)) và \(AB \bot BO = R\) nên AB là tiếp tuyến của đường tròn (O).

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

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