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Giải bài 2 trang 24 Chuyên đề học tập Toán 11 Chân trời sáng tạo

Cho đường tròn (O; R) và điểm I không nằm trên đường tròn.

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

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho đường tròn (O; R) và điểm I không nằm trên đường tròn. Với mỗi điểm A trên (O; R) ta xét hình vuông ABCD có tâm là I. Điểm C di động trên đường nào khi A di động trên đường tròn (O; R)?

Phương pháp giải - Xem chi tiết

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

Lời giải chi tiết

Hình vuông ABCD có tâm I.

Suy ra I là trung điểm AC.

🌠Do đó \(C{\rm{ }} = {\rm{ }}{Đ_I}\left( A \right).\)

🦋Gọi (O’; R’) là ảnh của \(\left( {O;{\rm{ }}R} \right)\) qua \({Đ_I}.\)

꧑Khi đó đường tròn \(\left( {O';{\rm{ }}R'} \right)\) có tâm \(O'{\rm{ }} = {\rm{ }}{Đ_I}\left( O \right),{\rm{ }}R'{\rm{ }} = {\rm{ }}R.\)

𒈔Vậy khi điểm A di động trên đường tròn \(\left( {O;{\rm{ }}R} \right)\) thì điểm C di động trên đường tròn \(\left( {O';{\rm{ }}R} \right),\) với O’ là điểm đối xứng với O qua tâm I.

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