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Giải bài 1 trang 115 SGK Toán 7 tập 2 - Cánh diều

Cho tam giác ABC và điểm O thỏa mãn OA = OB = OC. Chứng minh rằng O là giao điểm của ba đường trung trực của tam giác ABC.

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Đề bài

Cho tam giác ABC và điểm O thỏa mãn OA = OB = OC. Chứng minh rằng O là giao điểm của ba đường trung trực của tam giác ABC.

Phương pháp giải - Xem chi tiết

Tính chất đường trung trực của đoạn thẳng

Lời giải chi tiết

Ta có:

     OA = OB nên O nằm trên đường trung trực của đoạn thẳng AB (tính chất đường trung trực của đoạn thẳng). (1)

     OB = OC nên O nằm trên đường trung trực của đoạn thẳng BC (tính chất đường trung trực của đoạn thẳng). (2)

     OC = OA nên O nằm trên đường trung trực của đoạn thẳng AC (tính chất đường trung trực của đoạn thẳng). (3)

Từ (1), (2), và (3) suy ra O là giao điểm của ba đường trung trực của tam giác ABC.

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