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Giải bài tập 3 trang 82 SGK Toán 9 tập 1 - Chân trời sáng tạo

Cho tam giác ABC có hai đường cao BB’ và CC’. Gọi O là trung điểm BC. a) Chứng minh đường tròn tâm O bán kính OB’ đi qua B, C, C’; b) So sánh độ dài hai đoạn thẳng BC và B’C’.

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

Toán - Văn - Anh
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Đề bài

ꦕCho tam giác ABC có hai đường cao BB’ và CC’. Gọi O là trung điểm BC.

🦹a) Chứng minh đường tròn tâm O bán kính OB’ đi qua B, C, C’;

b) So sánh độ dài hai đoạn thẳng BC và B’C’.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Đọc kĩ dữ liệu đề bài để vẽ hình

- Áp dụng đ❀iểm cách đều ba đỉnh của một tam giác vuông là trung điểm của cạnh huyền của tam giác đó để chứng minh.

♊- Trong các dây của một đường tròn, đường kính là dây có độ dài lớn nhất để so sánh hai dây cung.

Lời giải chi tiết


🐼a) Xét tam giác BB’C vuông tại B’ có BC là cạnh huyền, O là trung điểm của BC

Suy ra O cách đều ba điểm B, B’, C hay OB = OB’ = OC. nên đường tròn tâm O bán kính OB’ đi qua B, C. Xét tam giác BCC’ vuông tại C’ có BC là cạnh huyền, O là trung điểm của BC Suy ra O cách đều ba điểm B, C, C’ hay OB = OC = OC’. Vậy đường tròn tâm O bán kính OB’ đi qua B, C, C’. b) Xét đường tròn tâm O, bán kính OB’, ta có: BC > B’C’ (do dây cung BC đi qua tâm O; B’C’ không đi qua tâm O).

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

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