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Giải bài 5 trang 102 sách bài tập toán 9 - Cánh diều tập 1

Cho hai đường tròn (O) và (O') có bán kính bằng nhau, cắt nhau tại A và B. Chứng minh tứ giác OAO'B là hình thoi; từ đó, suy ra AB cắt OO' tại trung điểm của mỗi đường.

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

Toán - Văn - Anh
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Đề bài

Cho hai đường tròn (O) và (O') có bán kính bằng nhau, cắt nhau tại A và B. Chứng minh tứ giác OAO'B là hình thoi; từ đó, suy ra AB cắt OO' tại trung điểm của mỗi đường.

Phương pháp giải - Xem chi tiết

Dựa vào dấu hiệu nhận biết: Tứ giác có 4 cạnh bằng nhau là hình thoi.

Lời giải chi tiết

Vì hai đường tròn (O) và (O') có bán kính bằng nhau, suy ra \(OA = OB = O'A = O'B\). Xét tứ giác OAO’B có: \(OA = OB = O'A = O'B\) nên OAO’B là hình thoi, do đó 2 đường chéo AB và OO’ cắt nhau tại trung điểm mỗi đường.

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

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