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Giải bài 31 trang 116 sách bài tập toán 9 - Cánh diều tập 1

Bạn An đố bạn Bình: “Hãy xác định tâm của đường tròn mà chỉ dùng ê ke.” Bạn Bình đã xác định tâm O của đường tròn như sau: - Lần thứ nhất: đặt góc vuông của ê ke tại điểm A, hai cạnh góc vuông của ê ke lần lượt cắt đường tròn tại hai điểm (gọi hai điểm đó là B, C); - Lần thứ hai: đặt góc vuông của ê ke tại điểm H, hai cạnh góc vuông của ê ke lần lượt cắt đường tròn tại hai điểm (gọi hai điểm đó là I, K). Quan sát Hình 34 và chứng minh rằng bằng cách làm hai lần như trên thì bạn Bình đã giải

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

Toán - Văn - Anh
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Đề bài

Bạn An đố bạn Bình: “Hãy xác định tâm của đường tròn mà chỉ dùng ê ke.” Bạn Bình đã xác định tâm O của đường tròn như sau: - Lần thứ nhất: đặt góc vuông của ê ke tại điểm A, hai cạnh góc vuông của ê ke lần lượt cắt đường tròn tại hai điểm (gọi hai điểm đó là B, C); - Lần thứ hai: đặt góc vuông của ê ke tại điểm H, hai cạnh góc vuông của ê ke lần lượt cắt đường tròn tại hai điểm (gọi hai điểm đó là I, K). Quan sát Hình 34 và chứng minh rằng bằng cách làm hai lần như trên thì bạn Bình đã giải được câu đố của bạn An.

Phương pháp giải - Xem chi tiết

Áp dụng: Góc nội tiếp chắn nửa đường tròn bằng 90⁰.

Lời giải chi tiết

Ta có \(\widehat {BAC} = \widehat {IHK} = 90^\circ \), mà 2 góc này nội tiếp đường tròn (O) nên chúng chắn nửa đường tròn. Do đó BC, IK là 2 đường kính của (O) và cắt nhau tại tâm O của đường tròn. Vậy bằng cách làm hai lần như trên thì bạn Bình đã giải được câu đố của bạn An.

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

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