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Quoc2006
2 năm trước
Cho tam giác ABC có ba góc nhọn nội tiếp (O; R). Các đường cao AK, BI của tam giác ABC cắt nhau tại H. Các đường thẳng AK và BI cắt đường tròn (O) lần lượt tại các điểm thứ hai là D và E. Chứng minh rằng: 1) Chứng minh tử giác ABKI nội tiếp. 2) Chứng minh IK//DE và OC vuông góc IK 3) Cho đường tròn (O) và dây AB cố định. Chứng minh rằng khi điểm C di chuyển trên cung lớn AB thì độ dài bán kính đường tròn ngoại tiếp tam giác CIK luôn không đổi.
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