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Giải mục 1 trang 84 SGK Toán 9 tập 1 - Kết nối tri thức

Cho tam giác ABC vuông tại A. Chứng minh rằng điểm A thuộc đường tròn đường kính BC.

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

Toán - Văn - Anh
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LT1

Video hướng dẫn giải

Trả lời câu hỏi Luyện tập 1 trang 84 SGK Toán 9 Kết nối tri thức

Cho tam giác ABC vuông tại A. Chứng minh rằng điểm A thuộc đường tròn đường kính BC.

Phương pháp giải:

Áp dụng tính chất đường trung tuyến trong tam giác vuông.

Lời giải chi tiết:

Gọi O là trung điểm của BC. Ta có AO là trung tuyến ứng với cạnh huyền nên \(OA = \frac{{BC}}{2} = OB = OC\). Suy ra A, B, C cùng thuộc đường tròn bán kính OB. Tâm O là trung điểm của BC nên BC là đường kính. Vậy A thuộc đường tròn đường kính BC.

VD1

Video hướng dẫn giải

Trả lời câu hỏi Vận dụng 1 trang 84 SGK Toán 9 Kết nối tri thức

Trong mặt phẳng tọa độ Oxy, cho các điểm A(3;0), B(- 2;0), C(0;4). Vẽ hình và cho biết trong các điểm đã cho, điểm nào nằm trên, điểm nào nằm trong, điểm nào nằm ngoài đường tròn (O; 3)?

Phương pháp giải:

Vẽ đường tròn (O; 3) và các điểm A(3;0), B(- 2;0), C(0;4). Sau đó dựa vào hình vẽ xác định điểm nào nằm trên, điểm nào nằm trong, điểm nào nằm ngoài đường tròn (O; 3).

Lời giải chi tiết:

Từ hình vẽ trên ta thấy: Điểm A nằm trên đường tròn, điểm B nằm trong đường tròn, điểm C nằm ngoài đường tròn.

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