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ngoc246lon
2 năm trước
Cho tam giác ABC có ba góc nhọn, nội tiếp đường tròn tâm O (AB < AC). Các đường cao AD và CF của tam giác ABC cắt nhau tại H. 1. Chứng minh tứ giác BFHD nội tiếp. Suy ra widehat{AHC} = 180^{0} - widehat{ABC} 2. Gọi M là điểm bất kì trên cung nhỏ BC của đường tròn (O) (M khác B và C) và N là điểm đối xứng của M qua AC. Chứng minh tứ giác AHCN nội tiếp. 3. Gọi I là giao điểm của AM và HC; J là giao điểm của AC và HN. Chứng minh widehat{AJI} = widehat{ANC} 4. Chứng minh rằng : OA vuông góc với IJ
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