TỔNG HỢP 30 ĐỀ THI TUYỂN SINH VÀO LỚP 10 CHUYÊN MÔN TOÁN

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Ngày đăng: 25/10/2014, 14:32

Câu 3. (3 điểm)Cho M là trung điểm của cung nhỏ AB của đường tròn tâm O (AB không phải là đường kính). C và D là 2 điểm phân biệt, thay đổi nằm giữa A và B. Các đường thẳng MC, MD cắt (O) tương ứng tại E, F khác M.a) Chứng minh các điểm C, D, E, F nằm trên một đường tròn.b) Gọi O1 và O2 lần lượt là tâm các đường tròn ngoại tiếp các tam giác ACE và BDF.Chứng minh rằng khi C và D thay đổi trên đoạn AB thì giao điểm của hai đường thẳng AO1 và BO2 là một điểm cố định.      !"#$% &'()*+", /01)2  3456789:;< :=0 >&&?@" A% BCD-E F#&GHI &J& K" LM%NO '(" LM%NO P?- ?I Q R :  <S  R  T : R :  <  R  S :RSE OR . FRS . 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