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Giải bài 23 trang 95 sách bài tập toán 11 - Cánh diều

Cho đoạn thẳng AB và mặt phẳng (P) sao cho \(\left( P \right) \bot AB\) và (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 đoạn thẳng AB và mặt phẳng (P) sao cho \(\left( P \right) \bot AB\) và (P) cắt đoạn thẳng AB tại điểm H thoả mãn HA = 4 cm, HB = 9 cm. Điểm C chuyển động trong mặt phẳng (P) thoả mãn \(\widehat {ACB} = {90^0}.\) Chứng minh rằng điểm C thuộc đường tròn tâm H bán kính 6 cm trong mặt phẳng (P).

Phương pháp giải - Xem chi tiết

Sử dụng hệ thức lượng trong tam giác vuông để tính độ dài HC.

Lời giải chi tiết

Vì \(AC \bot CB\) nên A, B, C không thẳng hàng.Ta có: \(\left( P \right) \bot AB,{\rm{ }}HC \subset \left( P \right)\) nên \(AB \bot HC.\)Xét \(\Delta ABC\) vuông tại C, đường cao CH. Áp dụng hệ thức lượng trong tam giác vuông ta có: \(H{C^2} = HA.HB = 4.9 = 36 \Rightarrow HC = 6\left( {{\rm{cm}}} \right).\)Vậy C thuộc đường tròn tâm H bán kính 6 cm 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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