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Giải bài tập 3 trang 78 SGK Toán 9 tập 2 - Cánh diều

Cho tam giác ABC nội tiếp đường tròn (O) thỏa mãn (widehat {ABC} = 60^circ ,widehat {ACB} = 70^circ .) Giả sử D là điểm thuộc cung BC không chứa A (D khác B và C). Tính số đo góc BDC.

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

Toán - Văn - Anh
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Đề bài

Cho tam giác ABC nội tiếp đường tròn (O) thỏa mãn \(\widehat {ABC} = 60^\circ ,\widehat {ACB} = 70^\circ .\) Giả sử D là điểm thuộc cung BC không chứa A (D khác B và C). Tính số đo góc BDC.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Bước 1: Áp dụng Định lý tổng 3 góc trong tam giác ABC để tính góc A. Bước 2: Áp dụng tổng 2 góc đối trong tứ giác nội tiếp đường tròn bằng \(180^\circ \) để tính góc BDC.

Lời giải chi tiết

Áp dụng Định lý tổng 3 góc trong tam giác ABC có: \(\begin{array}{l}\widehat {ABC} + \widehat {BCA} + \widehat {CAB} = 180^\circ \\\widehat {CAB} = 180^\circ  - \widehat {ABC} - \widehat {BCA}\\\widehat {CAB} = 180^\circ  - 60^\circ  - 70^\circ \\\widehat {CAB} = 50^\circ .\end{array}\) Vì tứ giác ABDC nội tiếp đường tròn nên tổng 2 góc đối bằng \(180^\circ \), do đó ta có: \(\begin{array}{l}\widehat A + \widehat D = 180^\circ \\\widehat D = 180^\circ  - \widehat A\\\widehat D = 180^\circ  - 50^\circ \\\widehat D = 130^\circ .\end{array}\) Vậy \(\widehat {BDC} = 130^\circ .\)

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