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Giải bài 3 trang 24 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Cho hình bình hành ABCD có AC cố định còn B di động trên (O; R). Hãy cho biết D di động trên đường nào.

♈Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

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Đề bài

🅰Cho hình bình hành ABCD có AC cố định còn B di động trên (O; R). Hãy cho biết D di động trên đường nào.

Phương pháp giải - Xem chi tiết

Vẽ ảnh của đường tròn (O; R) qua  Sau đó suy luận để chứng minh.

Lời giải chi tiết

Gọi I là tâm của hình bình hành ABCD, do đó I là trung điểm AC và BD.Do AC cố định nên I cũng cố định.Do I là trung điểm của BD nên \(D{\rm{ }} = {\rm{ }}{Đ_I}\left( B \right).\)Gọi \(\left( {O';{\rm{ }}R'} \right)\) là ảnh của \(\left( {O;{\rm{ }}R} \right)\) qua \({Đ_I}\)Khi đó đường tròn  có tâm \(O'{\rm{ }} = {\rm{ }}{Đ_I}\left( O \right),{\rm{ }}R'{\rm{ }} = {\rm{ }}R.\)Vậy khi điểm B di động trên (O; R) thì điểm D di động trên \(\left( {O';{\rm{ }}R} \right),\) với O’ là điểm đối xứng với O qua I.

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