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Giải bài tập 5 trang 117 SGK Toán 9 tập 1 - Cánh diều

Cho hai đường tròn (left( O right),left( I right)) cắt nhau tại hai điểm (A,B). Kẻ các đoạn thẳng (AC,AD) lần lượt là đường kính của hai đường tròn (left( O right),left( I right)). Chứng minh ba điểm (B,C,D) thẳng hàng.

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

Toán - Văn - Anh
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Đề bài

Cho hai đường tròn \(\left( O \right),\left( I \right)\) cắt nhau tại hai điểm \(A,B\). Kẻ các đoạn thẳng \(AC,AD\) lần lượt là đường kính của hai đường tròn \(\left( O \right),\left( I \right)\). Chứng minh ba điểm \(B,C,D\) thẳng hàng.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Dựa vào tính chất số đo góc nội tiếp để chứng minh.

Lời giải chi tiết

Xét đường tròn \(\left( I \right)\) có: \(\widehat {ABD}\) là góc nội tiếp chắn nửa đường tròn. Vậy \(\widehat {ABD} = 90^\circ \). Xét đường tròn \(\left( O \right)\) có: \(\widehat {ABC}\) là góc nội tiếp chắn nửa đường tròn. Vậy \(\widehat {ABC} = 90^\circ \). Ta có: \(\widehat {ABD} + \widehat {ABC} = 90^\circ  + 90^\circ  \Rightarrow \widehat {BDC} = 180^\circ \). Vậy ba điểm \(B,D,C\) thẳng hàng.

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