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Giải bài tập 5.21 trang 103 SGK Toán 9 tập 1 - Kết nối tri thức

Cho đường tròn (O) đi qua ba đỉnh A, B và C của một tam giác cân tại A, Chứng minh rằng đường thẳng đi qua A và song song với BC là một tiếp tuyến của (O).

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) đi qua ba đỉnh A, B và C của một tam giác cân tại A, Chứng minh rằng đường thẳng đi qua A và song song với BC là một tiếp tuyến của (O).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Chứng minh đường thẳng đi qua A là và song song với BC là tiếp tuyến tức là đường thẳng đó vuông góc với bán kính (hoặc đường kính) tại điểm A.

Lời giải chi tiết

Ta có đường thẳng AO là trục đối xứng của đường tròn. Nên B là điểm đối xứng của C qua AO. Gọi H là giao điểm của AO và BC. Khi đó ta có: AH \( \bot \) BC mà d // BC nên AH \( \bot \) d. Vậy d là một tiếp tuyến của đường tròn.

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

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