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Cho Δ ABC có ba góc nhọn nội tiếp (O;R). Giả sử các điểm B,C cố định và A di động trên (O) sao cho AB < AC < BC. Đường trung trực của đoạn thẳng AC cắt AB và BC lần lượt tại M và N. Chứng minh: OM.ON = R2. Bốn điểm M,N,P,Q cùng nằm trên một đường tròn. Giả sử hai đường tròn ngoại tiếp Δ BMN và Δ CPQ cắt nhau tại S và T. Chứng minh ba điểm S,T,O thẳng hàng.
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