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chuquynh123
2 năm trước
Cho đường tròn (O; 4 cm), đường kính AB. Lấy điểm H thuộc đoạn AO sao cho OH = 1 cm. Kẻ dây cung DC vuông góc với AB tại H. a) Chứng minh ∆ABC vuông và tính độ dài AC. b) Tiếp tuyến tại A của (O) cắt BC tại E. Chứng minh ∆CBD cân và EC/DH = EA/DB. c) Gọi I là trung điểm của EA; đoạn IB cắt (O) tại Q. Chứng minh CI là tiếp tuyến của (O) và từ đó suy ra ICQ = CBI. d) Tiếp tuyến tại B của (O) cắt IC tại F. Chứng minh ba đường thẳng IB, HC, AF đồng quy.
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