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Giải bài tập 7.19 trang 39 SGK Toán 9 tập 2 - Cùng khám phá

Cho đường tròn (O;R). Từ điểm M nằm ngoài đường tròn, vẽ hai tiếp tuyến tiếp xúc (O) tại A và B. Chứng minh rằng tứ giác MAOB là tứ giác nội tiếp.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

🏅Cho đường tròn (O;R). Từ điểm M nằm ngoài đường tròn, vẽ hai tiếp tuyến tiếp xúc (O) tại A và B. Chứng minh rằng tứ giác MAOB là tứ giác nội tiếp.

Phương pháp giải - Xem chi tiết

Đọc kĩ dữ liệu đề bài để vẽ hình.

﷽Nếu một đường thẳng là tiếp tuyến của một đường tròn thì nó vuông góc với bán kính đi qua tiếp điểm của đường tròn đó.

♏Nếu một tứ giác có tổng số đo hai góc đối diện bằng 180° thì tứ giác đó nội tiếp được đường tròn.

Lời giải chi tiết

Xét tứ giác MAOB có \(\widehat {MAO} = \widehat {MBO} = {90^o}\)(do tính chất tiếp tuyến) Suy ra \(\widehat {MAO} + \widehat {MBO} = {180^o}\) nên tứ giác MAOB nội tiếp.

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