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Giải bài 22 trang 95 sách bài tập toán 11 - Cánh diều

Cho mặt phẳng (P) và hai điểm A, B sao cho B thuộc (P) và 4 không thuộc (P).

💙Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

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

Cho mặt phẳng (P) và hai điểm A, B sao cho B thuộc (P) và 4 không thuộc (P). Điểm C chuyển động trên mặt phẳng (P) thoả mãn \(\widehat {ACB} = {90^0}.\) Chứng minh rằng C chuyển động trên một đường tròn cố định trong (P).

Phương pháp giải - Xem chi tiết

Sử dụng định lý ba đường vuông góc.

Lời giải chi tiết

Gọi H là hình chiếu của A trên (P).Khi đó H cố định và HC là hình chiếu của AC trên (P).Vì \(BC \bot AC\) nên theo định lí ba đường vuông góc ta có \(BC \bot HC.\)Do đó C chuyển động trên đường tròn đường kính HB cố định nằm trong (P).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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