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Giải bài 16 trang 90 sách bài tập toán 9 - Cánh diều tập 2

Cho đường tròn (O) ngoại tiếp tam giác đều ABC. Điểm E nằm trên cung nhỏ BC (E khác B và C). ED là tia đối của tia EB. Chứng minh EC là phân giác của góc AED và EA là phân giác của góc BEC.

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) ngoại tiếp tam giác đều ABC. Điểm E nằm trên cung nhỏ BC (E khác B và C). ED là tia đối của tia EB. Chứng minh EC là phân giác của góc AED và EA là phân giác của góc BEC.

Phương pháp giải - Xem chi tiết

💖Chứng minh \(\widehat {AEB} = \widehat {AEC} = {60^o}\)suy ra EA là phân giác của góc BEC.

Lời giải chi tiết

Ta có tứ giác ABEC nội tiếp đường tròn nên \(\widehat {CED} = \widehat {BAC} = {60^o}( = {180^o} - \widehat {BEC})\). Mặt khác \(\widehat {AEC} = \widehat {CED} = {60^o}\). Do đó, EC là phân giác của góc AED. Tương tự ta có \(\widehat {AEC} = \widehat {ABC} = {60^o}\) và \(\widehat {AEB} = \widehat {ACB} = {60^o}\). Do đó \(\widehat {AEB} = \widehat {AEC} = {60^o}\) hay EA là phân giác của góc BEC.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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